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Kasper Peeters
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Add sympy integration wrapper.
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‎core/packages/cdb/sympy/calculus.cnb‎

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"cell_type": "latex",
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"cells": [
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{
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"cell_id": 5114489047998022221,
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"cell_id": 7825517350706958358,
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"cell_origin": "client",
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"cell_type": "latex_view",
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"source": "\\package{cdb.sympy.calculus}{Glue to use SymPy calculus functionality on Cadabra expressions.}\n\nA lot of functionality in SymPy can be used on Cadabra expressions, but in order to correctly\nconvert from and to the SymPy expression form, we need a bridge. This package contains such\nbridging fuctions, which will ensure that e.g. tensor indices are handled correctly when\nfed through SymPy's scalar algebra algorithms.\n\n\\algorithm{diff}{Differentiate an expression with respect to a variable.}"
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"source": "\\package{cdb.sympy.calculus}{Use SymPy calculus functionality on Cadabra expressions.}\n\nA lot of functionality in SymPy can be used on Cadabra expressions, but in order to correctly\nconvert from and to the SymPy expression form, we need a bridge. This package contains such\nbridging fuctions, which will ensure that e.g. tensor indices are handled correctly when\nfed through SymPy's scalar algebra algorithms.\n\n\\algorithm{diff}{Differentiate an expression with respect to a variable.}"
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}
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],
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"hidden": true,
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"source": "\\package{cdb.sympy.calculus}{Glue to use SymPy calculus functionality on Cadabra expressions.}\n\nA lot of functionality in SymPy can be used on Cadabra expressions, but in order to correctly\nconvert from and to the SymPy expression form, we need a bridge. This package contains such\nbridging fuctions, which will ensure that e.g. tensor indices are handled correctly when\nfed through SymPy's scalar algebra algorithms.\n\n\\algorithm{diff}{Differentiate an expression with respect to a variable.}"
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"source": "\\package{cdb.sympy.calculus}{Use SymPy calculus functionality on Cadabra expressions.}\n\nA lot of functionality in SymPy can be used on Cadabra expressions, but in order to correctly\nconvert from and to the SymPy expression form, we need a bridge. This package contains such\nbridging fuctions, which will ensure that e.g. tensor indices are handled correctly when\nfed through SymPy's scalar algebra algorithms.\n\n\\algorithm{diff}{Differentiate an expression with respect to a variable.}"
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},
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{
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"cell_id": 3804610120254550473,
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"cell_origin": "client",
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"cell_type": "input",
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"source": "def diff(ex1, ex2):\n ret = $@(ex1)$\n sb = SympyBridge(ret)\n sb.from_sympy( str(sympy.diff( sb.to_sympy(), ex2 ) ) )\n return ret"
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},
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{
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"cell_id": 12308609622224851480,
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"cell_origin": "client",
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"cell_type": "latex",
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"cells": [
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{
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"cell_id": 13996360633394007671,
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"cell_origin": "client",
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"cell_type": "latex_view",
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"source": "A typical example, differentiating with respect to a single variable:"
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}
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],
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"hidden": true,
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"source": "A typical example, differentiating with respect to a single variable:"
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},
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{
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"cell_id": 1389897799554975903,
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"cell_origin": "client",
@@ -59,10 +74,143 @@
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"ignore_on_import": true,
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"source": "ex:=\\sin(x) A_{\\mu}(x);\ndiff(ex, $x$);"
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},
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{
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"cell_id": 6234003092100779795,
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"cell_origin": "client",
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"cell_type": "latex",
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"cells": [
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{
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"cell_id": 10150353556520051186,
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"cell_origin": "client",
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"cell_type": "latex_view",
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"source": "\\algorithm{integrate}{Integrate a definite or indefinite integral.}\n\nThis function mimics the SymPy \\verb|integrate| function, except that all\nmathematical expressions need to be Cadabra expressions. Indefinite integration\nis done by passing an argument which is just an expression, while definite\nintegration is done by passing a tuple consisting of the integration variable,\nthe starting point and the end point."
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}
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],
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"hidden": true,
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"source": "\\algorithm{integrate}{Integrate a definite or indefinite integral.}\n\nThis function mimics the SymPy \\verb|integrate| function, except that all\nmathematical expressions need to be Cadabra expressions. Indefinite integration\nis done by passing an argument which is just an expression, while definite\nintegration is done by passing a tuple consisting of the integration variable,\nthe starting point and the end point."
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},
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{
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"cell_id": 15467993639628642890,
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"cell_origin": "client",
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"cell_type": "input",
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"source": "def integrate(ex1, *args):\n ret = $@(ex1)$\n sb = SympyBridge(ret)\n iranges = []\n for arg in args:\n if isinstance(arg, tuple):\n # print(arg)\n sbtmp = SympyBridge(arg[0])\n tpl = (sbtmp.to_sympy(), arg[1], arg[2])\n iranges.append(tpl)\n # print(iranges)\n sb.from_sympy( str(sympy.integrate( sb.to_sympy(), *iranges) ) )\n else:\n sbtmp = SympyBridge(arg)\n sb.from_sympy( str(sympy.integrate( sb.to_sympy(), sbtmp.to_sympy() ) ))\n return ret"
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},
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{
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"cell_id": 3801120048138997797,
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"cell_origin": "client",
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"cell_type": "latex",
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"cells": [
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{
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"cell_id": 13060402605556641930,
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"cell_origin": "client",
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"cell_type": "latex_view",
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"source": "The following is an example of a definite integration:"
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}
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],
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"hidden": true,
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"source": "The following is an example of a definite integration:"
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},
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{
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"cell_id": 14525293143474443676,
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"cell_origin": "client",
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"cell_type": "input",
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"cells": [
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{
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"cell_id": 12012117006062441490,
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"cell_origin": "server",
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"cell_type": "latex_view",
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"cells": [
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{
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"cell_id": 316157390348515815,
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"cell_origin": "server",
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"cell_type": "input_form",
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"source": " 27/2 "
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}
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],
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"source": "\\begin{dmath*}{}\\frac{27}{2}\\end{dmath*}"
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}
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],
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"ignore_on_import": true,
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"source": "integrate($x**2 y$, ($x$, 0, 3), ($y$, 0, 1) );"
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},
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{
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"cell_id": 2354178610469859185,
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"cell_origin": "client",
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"cell_type": "latex",
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"cells": [
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{
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"cell_id": 17727729829154494875,
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"cell_origin": "client",
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"cell_type": "latex_view",
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"source": "Here is an indefinite integration:"
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}
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],
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"hidden": true,
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"source": "Here is an indefinite integration:"
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},
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{
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"cell_id": 2273072162227922772,
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"cell_origin": "client",
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"cell_type": "input",
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"cells": [
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{
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"cell_id": 15728598564050855914,
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"cell_origin": "server",
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"cell_type": "latex_view",
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"cells": [
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{
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"cell_id": 13682162971051715272,
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"cell_origin": "server",
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"cell_type": "input_form",
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"source": " 1/3 (x)**3 y"
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}
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],
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"source": "\\begin{dmath*}{}\\frac{1}{3}{x}^{3} y\\end{dmath*}"
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}
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],
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"source": "integrate($x**2$, $x$, $y$);"
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},
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{
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"cell_id": 14437617558705092816,
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"cell_origin": "client",
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"cell_type": "latex",
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"cells": [
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{
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"cell_id": 9935958107203452733,
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"cell_origin": "client",
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"cell_type": "latex_view",
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"source": "Mixed versions are also possible:"
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}
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],
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"hidden": true,
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"source": "Mixed versions are also possible:"
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},
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{
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"cell_id": 6556436360376410122,
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"cell_origin": "client",
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"cell_type": "input",
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"cells": [
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{
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"cell_id": 4095815210246821736,
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"cell_origin": "server",
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"cell_type": "latex_view",
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"cells": [
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{
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"cell_id": 13733098240311066994,
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"cell_origin": "server",
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"cell_type": "input_form",
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"source": " 1/4 (y)**2"
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}
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],
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"source": "\\begin{dmath*}{}\\frac{1}{4}{y}^{2}\\end{dmath*}"
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}
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],
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"source": "integrate($x y$, ($x$, 0, 1), $y$);"
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},
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{
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"cell_id": 14261374590043911759,
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"cell_origin": "client",
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"cell_type": "input",
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"source": ""
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}
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],

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