Commit be6ae3a8 authored by Dennis Müller's avatar Dennis Müller

generated files

parent 7b424770
......@@ -3,17 +3,17 @@
</constant><constant name="Associative">
</constant><constant name="AdditiveInverse">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="Distributive">
</constant><constant name="AdditiveUnital">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="WithBasis">
</constant><constant name="AdditiveAssociative">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
......@@ -23,42 +23,42 @@
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="Unital">
</constant><constant name="Distributive">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="AdditiveAssociative">
</constant><constant name="WithBasis">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="AdditiveInverse">
</constant><constant name="Commutative">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="AdditiveUnital">
</constant><constant name="Unital">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="Inverse">
</constant><constant name="Facade">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="Commutative">
</constant><constant name="Associative">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="NoZeroDivisors">
</constant><constant name="Infinite">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="Finite">
</constant><constant name="Enumerated">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
......@@ -68,42 +68,42 @@
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="FiniteDimensional">
</constant><constant name="Inverse">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="WellGenerated">
</constant><constant name="Finite">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="Division">
</constant><constant name="NoZeroDivisors">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="Infinite">
</constant><constant name="Division">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="GAP">
</constant><constant name="Irreducible">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="Facade">
</constant><constant name="Connected">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="Connected">
</constant><constant name="WellGenerated">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="JTrivial">
</constant><constant name="FiniteDimensional">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
......@@ -113,7 +113,7 @@
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="Compact">
</constant><constant name="JTrivial">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
......@@ -123,7 +123,7 @@
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
</constant><constant name="Irreducible">
</constant><constant name="Compact">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="Types" name="prop"></om:OMS></om:OMOBJ></type>
......
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="CachedRepresentation" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Sage"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1960.79.0:2000.80.1"/></metadata></theory></omdoc>
\ No newline at end of file
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="CachedRepresentation" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Sage"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1960.79.0:1998.80.-1"/></metadata></theory></omdoc>
\ No newline at end of file
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Convenient" base="http://www.sagemath.org/"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#317.14.0:392.17.1"/></metadata><import from="http://cds.omdoc.org/urtheories?PLF"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#340.15.2:356.15.18"/></metadata></import><import from="http://mathhub.info/MitM/Foundation?Math"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#360.16.2:389.16.31"/></metadata></import></theory></omdoc>
\ No newline at end of file
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Convenient" base="http://www.sagemath.org/"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#317.14.0:390.17.-1"/></metadata><import from="http://cds.omdoc.org/urtheories?PLF"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#340.15.2:356.15.18"/></metadata></import><import from="http://mathhub.info/MitM/Foundation?Math"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#360.16.2:389.16.31"/></metadata></import></theory></omdoc>
\ No newline at end of file
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PermutationGroup_generic" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Sage"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1735.72.0:1957.76.1"/></metadata><import from="http://www.sagemath.org/?group.FiniteGroup"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1779.73.2:1806.73.29"/></metadata></import><constant name="init">
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PermutationGroup_generic" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Sage"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1735.72.0:1955.76.-1"/></metadata><import from="http://www.sagemath.org/?group.FiniteGroup"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1779.73.2:1806.73.29"/></metadata></import><constant name="init">
<metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1810.74.2:1854.74.46"/></metadata>
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1816.74.8:1851.74.43"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
......
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PermutationGroup_unique" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Sage"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#2004.82.0:2118.85.1"/></metadata><import from="http://www.sagemath.org/?CachedRepresentation"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#2047.83.2:2077.83.32"/></metadata></import><import from="http://www.sagemath.org/?PermutationGroup_generic"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#2081.84.2:2115.84.36"/></metadata></import></theory></omdoc>
\ No newline at end of file
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PermutationGroup_unique" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Sage"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#2004.82.0:2116.85.-1"/></metadata><import from="http://www.sagemath.org/?CachedRepresentation"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#2047.83.2:2077.83.32"/></metadata></import><import from="http://www.sagemath.org/?PermutationGroup_generic"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#2081.84.2:2115.84.36"/></metadata></import></theory></omdoc>
\ No newline at end of file
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PythonBasicTypes" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Convenient"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#395.19.0:684.29.1"/></metadata><constant name="python_type">
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PythonBasicTypes" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Convenient"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#395.19.0:682.29.-1"/></metadata><constant name="python_type">
<metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#439.20.2:459.20.22"/></metadata>
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://cds.omdoc.org/urtheories" module="Typed" name="type"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#453.20.16:456.20.19"/></metadata></om:OMS></om:OMOBJ></type>
......
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PythonClass" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Convenient"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#908.38.0:1318.49.1"/></metadata><import from="http://www.sagemath.org/?PythonBasicTypes"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#946.39.2:972.39.28"/></metadata></import><theory name="PythonClassTheory" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Convenient">
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PythonClass" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Convenient"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#908.38.0:1316.49.-1"/></metadata><import from="http://www.sagemath.org/?PythonBasicTypes"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#946.39.2:972.39.28"/></metadata></import><theory name="PythonClassTheory" base="http://www.sagemath.org/">
<metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#976.40.2:1273.47.3"/></metadata><constant name="docstring">
<metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#976.40.2:1271.47.1"/></metadata><constant name="docstring">
<metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1107.43.4:1132.43.29"/></metadata>
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1119.43.16:1129.43.26"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
......@@ -18,4 +18,9 @@
</constant>
</theory><derived feature="FromTheory" name="[http://www.sagemath.org/?PythonClass/PythonClassTheory]" base="http://www.sagemath.org/"><type><om:OML name="pyclass"><type><om:OMS base="http://www.sagemath.org/" module="PythonClass/PythonClassTheory"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1297.48.23:1313.48.39"/></metadata></om:OMS></type></om:OML></type></derived></theory></omdoc>
\ No newline at end of file
</theory><constant name="FromTheory">
<metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1276.48.2:1316.48.42"/></metadata>
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="PythonClass/PythonClassTheory"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1297.48.23:1313.48.39"/></metadata></om:OMS></om:OMOBJ></type>
</constant></theory></omdoc>
\ No newline at end of file
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PythonFunction" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Convenient"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#686.31.0:906.36.1"/></metadata><import from="http://www.sagemath.org/?PythonBasicTypes"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#727.32.2:753.32.28"/></metadata></import><constant name="pyfunction">
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PythonFunction" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Convenient"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#686.31.0:904.36.-1"/></metadata><import from="http://www.sagemath.org/?PythonBasicTypes"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#727.32.2:753.32.28"/></metadata></import><constant name="pyfunction">
<metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#757.33.2:790.33.35"/></metadata>
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#770.33.15:787.33.32"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
......
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PythonUnknownType" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Convenient"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1322.51.0:1423.54.1"/></metadata><import from="http://www.sagemath.org/?PythonBasicTypes"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1366.52.2:1392.52.28"/></metadata></import><constant name="pyunknown">
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="PythonUnknownType" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Convenient"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1322.51.0:1421.54.-1"/></metadata><import from="http://www.sagemath.org/?PythonBasicTypes"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1366.52.2:1392.52.28"/></metadata></import><constant name="pyunknown">
<metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1396.53.2:1421.53.27"/></metadata>
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://www.sagemath.org/" module="PythonBasicTypes" name="python_type"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1408.53.14:1418.53.24"/></metadata></om:OMS></om:OMOBJ></type>
......
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Python" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Convenient"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1427.56.0:1573.61.1"/></metadata><import from="http://www.sagemath.org/?PythonBasicTypes"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1460.57.2:1486.57.28"/></metadata></import><import from="http://www.sagemath.org/?PythonFunction"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1490.58.2:1514.58.26"/></metadata></import><import from="http://www.sagemath.org/?PythonClass"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1518.59.2:1539.59.23"/></metadata></import><import from="http://www.sagemath.org/?PythonUnknownType"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1543.60.2:1570.60.29"/></metadata></import></theory></omdoc>
\ No newline at end of file
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Python" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Convenient"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1427.56.0:1571.61.-1"/></metadata><import from="http://www.sagemath.org/?PythonBasicTypes"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1460.57.2:1486.57.28"/></metadata></import><import from="http://www.sagemath.org/?PythonFunction"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1490.58.2:1514.58.26"/></metadata></import><import from="http://www.sagemath.org/?PythonClass"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1518.59.2:1539.59.23"/></metadata></import><import from="http://www.sagemath.org/?PythonUnknownType"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1543.60.2:1570.60.29"/></metadata></import></theory></omdoc>
\ No newline at end of file
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Sage" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Python"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1579.63.0:1693.67.1"/></metadata><constant name="sage_type">
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Sage" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Python"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1579.63.0:1691.67.-1"/></metadata><constant name="sage_type">
<metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1606.64.2:1624.64.20"/></metadata>
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://cds.omdoc.org/urtheories" module="Typed" name="type"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#1618.64.14:1621.64.17"/></metadata></om:OMS></om:OMOBJ></type>
......
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="TransitiveGroup" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Sage"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#2120.87.0:2301.91.1"/></metadata><import from="http://www.sagemath.org/?PermutationGroup_unique"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#2155.88.2:2188.88.35"/></metadata></import><constant name="init">
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="TransitiveGroup" base="http://www.sagemath.org/" meta="http://www.sagemath.org/?Sage"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#2120.87.0:2299.91.-1"/></metadata><import from="http://www.sagemath.org/?PermutationGroup_unique"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#2155.88.2:2188.88.35"/></metadata></import><constant name="init">
<metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#2192.89.2:2240.89.50"/></metadata>
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#2198.89.8:2237.89.47"/></metadata>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="apply"></om:OMS>
......
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Types" base="http://www.sagemath.org/" meta="http://cds.omdoc.org/urtheories?PLF"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#77.4.0:230.10.1"/></metadata><constant name="object">
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Types" base="http://www.sagemath.org/" meta="http://cds.omdoc.org/urtheories?PLF"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#77.4.0:228.10.-1"/></metadata><constant name="object">
<metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#103.5.1:118.5.16"/></metadata>
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMS base="http://cds.omdoc.org/urtheories" module="Typed" name="type"><metadata><link rel="http://cds.omdoc.org/mmt?metadata?sourceRef" resource="http://www.sagemath.org/sage.mmt#112.5.10:115.5.13"/></metadata></om:OMS></om:OMOBJ></type>
......
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Algebras" base="http://www.sagemath.org/content/categories/additive_groups/AdditiveGroups" meta="http://www.sagemath.org/?Types"><import from="http://www.sagemath.org/?Axioms"></import><import from="http://www.sagemath.org/?Structures"></import><import from="http://www.sagemath.org/content/categories/algebras_with_basis?AlgebrasWithBasis"></import><import from="http://www.sagemath.org/content/categories/additive_semigroups/AdditiveSemigroups?Algebras"></import><import from="http://www.sagemath.org/content/categories/additive_magmas/AdditiveMagmas/AdditiveUnital?Algebras"></import><omdoc name="Parent Methods"><constant name="parent.group">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
<om:OMS base="http://www.sagemath.org/" module="Types" name="object"></om:OMS><om:OMS base="http://www.sagemath.org/" module="Types" name="object"></om:OMS>
</om:OMA></om:OMOBJ></type>
</constant><opaque format="text">
Return the underlying group of the group algebra.
EXAMPLES::
sage: GroupAlgebras(QQ).example(GL(3, GF(11))).group()
General Linear Group of degree 3 over Finite Field of size 11
sage: SymmetricGroup(10).algebra(QQ).group()
Symmetric group of order 10! as a permutation group
</opaque></omdoc></theory></omdoc>
\ No newline at end of file
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Finite" base="http://www.sagemath.org/content/categories/additive_groups/AdditiveGroups" meta="http://www.sagemath.org/?Types"><import from="http://www.sagemath.org/?Axioms"></import><import from="http://www.sagemath.org/?Structures"></import><import from="http://www.sagemath.org/content/categories/additive_groups?AdditiveGroups"></import><import from="http://www.sagemath.org/content/categories/finite_sets?FiniteSets"></import></theory></omdoc>
\ No newline at end of file
<omdoc xmlns="http://omdoc.org/ns" xmlns:om="http://www.openmath.org/OpenMath"><theory name="Algebras" base="http://www.sagemath.org/content/categories/additive_groups/AdditiveGroups/Finite" meta="http://www.sagemath.org/?Types"><import from="http://www.sagemath.org/?Axioms"></import><import from="http://www.sagemath.org/?Structures"></import><import from="http://www.sagemath.org/content/categories/additive_groups/AdditiveGroups?Algebras"></import><import from="http://www.sagemath.org/content/categories/finite_dimensional_algebras_with_basis?FiniteDimensionalAlgebrasWithBasis"></import><import from="http://www.sagemath.org/content/categories/finite_sets/FiniteSets?Algebras"></import></theory></omdoc>
\ No newline at end of file
......@@ -319,42 +319,7 @@
</om:OMA></om:OMOBJ></type>
</constant><opaque format="text">
Return the sum of ``x`` and ``y``.
The binary addition operator of this additive magma.
INPUT:
- ``x``, ``y`` -- elements of this additive magma
EXAMPLES::
sage: S = CommutativeAdditiveSemigroups().example()
sage: (a,b,c,d) = S.additive_semigroup_generators()
sage: S.summation(a, b)
a + b
A parent in ``AdditiveMagmas()`` must
either implement :meth:`.summation` in the parent class or
``_add_`` in the element class. By default, the addition
method on elements ``x._add_(y)`` calls
``S.summation(x,y)``, and reciprocally.
As a bonus effect, ``S.summation`` by itself models the
binary function from ``S`` to ``S``::
sage: bin = S.summation
sage: bin(a,b)
a + b
Here, ``S.summation`` is just a bound method. Whenever
possible, it is recommended to enrich ``S.summation`` with
extra mathematical structure. Lazy attributes can come
handy for this.
.. TODO:: Add an example.
</opaque></omdoc><omdoc name="Subcategory Methods"><constant name="subcategory.AdditiveAssociative">
</constant></omdoc><omdoc name="Subcategory Methods"><constant name="subcategory.AdditiveAssociative">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
......@@ -483,114 +448,7 @@ File: sage/misc/cachefunc.pyx (starting at line 2607)
</om:OMA></om:OMOBJ></type>
</constant><opaque format="text">CachedMethod(f, name=None, key=None, do_pickle=None)
File: sage/misc/cachefunc.pyx (starting at line 2607)
A decorator that creates a cached version of an instance
method of a class.
.. NOTE::
For proper behavior, the method must be a pure function (no side
effects). Arguments to the method must be hashable or transformed into
something hashable using ``key`` or they must define
:meth:`sage.structure.sage_object.SageObject._cache_key`.
EXAMPLES::
sage: class Foo(object):
....: @cached_method
....: def f(self, t, x=2):
....: print('computing')
....: return t**x
sage: a = Foo()
The example shows that the actual computation
takes place only once, and that the result is
identical for equivalent input::
sage: res = a.f(3, 2); res
computing
9
sage: a.f(t = 3, x = 2) is res
True
sage: a.f(3) is res
True
Note, however, that the :class:`CachedMethod` is replaced by a
:class:`CachedMethodCaller` or :class:`CachedMethodCallerNoArgs`
as soon as it is bound to an instance or class::
sage: P.&lt;a,b,c,d&gt; = QQ[]
sage: I = P*[a,b]
sage: type(I.__class__.gens)
&lt;type 'sage.misc.cachefunc.CachedMethodCallerNoArgs'&gt;
So, you would hardly ever see an instance of this class alive.
The parameter ``key`` can be used to pass a function which creates a
custom cache key for inputs. In the following example, this parameter is
used to ignore the ``algorithm`` keyword for caching::
sage: class A(object):
....: def _f_normalize(self, x, algorithm): return x
....: @cached_method(key=_f_normalize)
....: def f(self, x, algorithm='default'): return x
sage: a = A()
sage: a.f(1, algorithm=&quot;default&quot;) is a.f(1) is a.f(1, algorithm=&quot;algorithm&quot;)
True
The parameter ``do_pickle`` can be used to enable pickling of the cache.
Usually the cache is not stored when pickling::
sage: class A(object):
....: @cached_method
....: def f(self, x): return None
sage: import __main__
sage: __main__.A = A
sage: a = A()
sage: a.f(1)
sage: len(a.f.cache)
1
sage: b = loads(dumps(a))
sage: len(b.f.cache)
0
When ``do_pickle`` is set, the pickle contains the contents of the cache::
sage: class A(object):
....: @cached_method(do_pickle=True)
....: def f(self, x): return None
sage: __main__.A = A
sage: a = A()
sage: a.f(1)
sage: len(a.f.cache)
1
sage: b = loads(dumps(a))
sage: len(b.f.cache)
1
Cached methods can not be copied like usual methods, see :trac:`12603`.
Copying them can lead to very surprising results::
sage: class A:
....: @cached_method
....: def f(self):
....: return 1
sage: class B:
....: g=A.f
....: def f(self):
....: return 2
sage: b=B()
sage: b.f()
2
sage: b.g()
1
sage: b.f()
1
</opaque><constant name="subcategory.AdditiveUnital">
</constant><constant name="subcategory.AdditiveUnital">
<type><om:OMOBJ xmlns:om="http://www.openmath.org/OpenMath"><om:OMA>
<om:OMS base="http://cds.omdoc.org/urtheories" module="LambdaPi" name="arrow"></om:OMS>
......@@ -601,111 +459,4 @@ File: sage/misc/cachefunc.pyx (starting at line 2607)
</om:OMA></om:OMOBJ></type>
</constant><opaque format="text">CachedMethod(f, name=None, key=None, do_pickle=None)
File: sage/misc/cachefunc.pyx (starting at line 2607)
A decorator that creates a cached version of an instance
method of a class.
.. NOTE::
For proper behavior, the method must be a pure function (no side
effects). Arguments to the method must be hashable or transformed into
something hashable using ``key`` or they must define
:meth:`sage.structure.sage_object.SageObject._cache_key`.
EXAMPLES::
sage: class Foo(object):
....: @cached_method
....: def f(self, t, x=2):
....: print('computing')
....: return t**x
sage: a = Foo()
The example shows that the actual computation
takes place only once, and that the result is
identical for equivalent input::
sage: res = a.f(3, 2); res
computing
9
sage: a.f(t = 3, x = 2) is res
True
sage: a.f(3) is res
True
Note, however, that the :class:`CachedMethod` is replaced by a
:class:`CachedMethodCaller` or :class:`CachedMethodCallerNoArgs`
as soon as it is bound to an instance or class::
sage: P.&lt;a,b,c,d&gt; = QQ[]
sage: I = P*[a,b]
sage: type(I.__class__.gens)
&lt;type 'sage.misc.cachefunc.CachedMethodCallerNoArgs'&gt;
So, you would hardly ever see an instance of this class alive.
The parameter ``key`` can be used to pass a function which creates a
custom cache key for inputs. In the following example, this parameter is
used to ignore the ``algorithm`` keyword for caching::
sage: class A(object):
....: def _f_normalize(self, x, algorithm): return x
....: @cached_method(key=_f_normalize)
....: def f(self, x, algorithm='default'): return x
sage: a = A()
sage: a.f(1, algorithm=&quot;default&quot;) is a.f(1) is a.f(1, algorithm=&quot;algorithm&quot;)
True
The parameter ``do_pickle`` can be used to enable pickling of the cache.
Usually the cache is not stored when pickling::
sage: class A(object):
....: @cached_method
....: def f(self, x): return None
sage: import __main__
sage: __main__.A = A
sage: a = A()
sage: a.f(1)
sage: len(a.f.cache)
1
sage: b = loads(dumps(a))
sage: len(b.f.cache)
0
When ``do_pickle`` is set, the pickle contains the contents of the cache::
sage: class A(object):
....: @cached_method(do_pickle=True)
....: def f(self, x): return None
sage: __main__.A = A