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Kasper Peeters
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Add limit and series. Improve web docs.
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‎client_server/notebook.tex‎

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@@ -32,6 +32,8 @@
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%\makeatletter\def\old@comma{,}\catcode`\,=13 \def,{%
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%\ifmmode\old@comma\discretionary{}{}{}\else\old@comma\fi}\makeatother
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\newcommand{\bigO}{{\cal O}}
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% Math expressions wrapped in \brwrap will get typeset with
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% round brackets around them, which have the appropriate size.
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% The expression itself can still be broken over multiple lines.

‎core/DisplaySympy.cc‎

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@@ -41,7 +41,7 @@ DisplaySympy::DisplaySympy(const Kernel& kernel, const Ex& e)
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{"\\sqrt", "sqrt" },
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{"\\equals", "Eq" },
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{"\\infty", "sympy.oo"},
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{"\\infty", "oo"},
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{"\\hbar", "hbar"},
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{"\\alpha", "alpha" },

‎core/packages/cdb/sympy/calculus.cnb‎

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@@ -80,6 +80,7 @@
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"source": "\\begin{dmath*}{}-\\sin{y} \\cos{x}\\end{dmath*}"
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}
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],
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"ignore_on_import": true,
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"source": "diff($\\sin(x)\\cos(y)$, $x$, $y$);"
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},
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{
@@ -176,6 +177,7 @@
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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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"ignore_on_import": true,
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"source": "integrate($x**2$, $x$, $y$);"
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},
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{
@@ -213,12 +215,146 @@
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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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"ignore_on_import": true,
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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": 15496749977354253222,
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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": 11565454487843639642,
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"cell_origin": "client",
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"cell_type": "latex_view",
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"source": "\\algorithm{limit}{Take the limit of an expression.}\n\nThis function mimics the SymPy \\verb|limit| function, except that all\nmathematical expressions need to be Cadabra expressions."
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}
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],
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"source": "\\algorithm{limit}{Take the limit of an expression.}\n\nThis function mimics the SymPy \\verb|limit| function, except that all\nmathematical expressions need to be Cadabra expressions."
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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": "def limit(ex, v, loc, *args):\n ret = $@(ex)$\n sbex = SympyBridge(ret)\n sbvar = SympyBridge(v).to_sympy()\n sbloc = SympyBridge(loc).to_sympy() if isinstance(loc, Ex) else loc\n sbex.from_sympy( str(sympy.limit( sbex.to_sympy(), sbvar, sbloc ) ) )\n return ret"
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},
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{
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"cell_id": 15671206733202710229,
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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": 8723327984628819396,
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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": 3839762579849277582,
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"cell_origin": "server",
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"cell_type": "input_form",
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"source": "1"
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}
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],
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"source": "\\begin{dmath*}{}1\\end{dmath*}"
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}
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],
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"ignore_on_import": true,
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"source": "limit($\\sin(x)/x$, $x$, 0);"
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},
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{
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"cell_id": 4403018984250840411,
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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": 11512538112824887976,
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"cell_origin": "client",
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"cell_type": "latex_view",
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"source": "\\algorithm{series}{Construct a Taylor series.}\n\nThis function mimics the SymPy \\verb|series| function, except that all\nmathematical expressions need to be Cadabra expressions."
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}
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],
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"hidden": true,
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"source": "\\algorithm{series}{Construct a Taylor series.}\n\nThis function mimics the SymPy \\verb|series| function, except that all\nmathematical expressions need to be Cadabra expressions."
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},
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{
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"cell_id": 1152336426546868041,
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"cell_origin": "client",
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"cell_type": "input",
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"source": "def series(ex, v, loc, order_, *args):\n ret = $@(ex)$\n sbex = SympyBridge(ret)\n sbvar = SympyBridge(v).to_sympy()\n sbloc = SympyBridge(loc).to_sympy() if isinstance(loc, Ex) else loc\n tmp = str(sympy.series( sbex.to_sympy(), sbvar, sbloc, order_ ) )\n tmp = tmp.replace(\"O(\", r\"\\bigO(\")\n sbex.from_sympy( tmp )\n return ret"
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},
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{
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"cell_id": 796023660136979964,
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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": 3415134206898553614,
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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": 17449491732516654073,
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"cell_origin": "server",
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"cell_type": "input_form",
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"source": "1 - 1/6 (x)**2 + \\bigO((x)**4)"
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}
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],
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"source": "\\begin{dmath*}{}1 - \\frac{1}{6}{x}^{2}+\\bigO\\left({x}^{4}\\right)\\end{dmath*}"
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}
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],
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"ignore_on_import": true,
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"source": "q=series($\\sin(x)/x$, $x$, 0, 4);"
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},
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{
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"cell_id": 12877610158835516880,
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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": 16889301844141721001,
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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": 15333461881261583200,
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"cell_origin": "server",
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"cell_type": "input_form",
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"source": "1 - 1/6 (x)**2"
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}
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],
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"source": "\\begin{dmath*}{}1 - \\frac{1}{6}{x}^{2}\\end{dmath*}"
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}
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],
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"ignore_on_import": true,
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"source": "substitute(q, $\\bigO(A??) ->0$);"
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},
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{
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"cell_id": 6061726248509003999,
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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": 8301222040948595643,
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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": 6578198996268257631,
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"cell_origin": "server",
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"cell_type": "input_form",
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"source": " 1/2 \\sqrt(2)-\\sqrt(2) ( 1/2 x - 1/8 \\pi) + \\bigO((x - 1/4 \\pi)**2 , {x, 1/4 \\pi})"
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}
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],
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"source": "\\begin{dmath*}{}\\frac{1}{2}\\sqrt{2}-\\sqrt{2} \\left(\\frac{1}{2}x - \\frac{1}{8}\\pi\\right)+\\bigO\\left({\\left(x - \\frac{1}{4}\\pi\\right)}^{2} , \\discretionary{}{}{}\\left[x,~\\discretionary{}{}{} \\frac{1}{4}\\pi\\right]\\right)\\end{dmath*}"
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}
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],
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"ignore_on_import": true,
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"source": "series($\\cos(x)$, $x$, $\\pi/4$, 2);"
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},
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{
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"cell_id": 16349293761953373413,
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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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],

‎frontend/common/preamble.tex‎

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\renewcommand{\author}[1]{{\bfseries \detokenize{#1}}}
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\newcommand{\email}[1]{, {\tt \detokenize{#1}}}
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\newcommand{\bigO}{{\cal O}}
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% \newcommand{\sequence}[2]{{#1}\ldots{#2}}
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% Math expressions wrapped in \brwrap will get typeset with

‎tests/sympy_cdb.cdb‎

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@@ -55,4 +55,15 @@ def test04():
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print("Test 04 passed")
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test04()
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from cdb.sympy.calculus import integrate
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def test05():
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__cdbkernel__=create_scope()
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ex:= \exp(-x);
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tst = integrate(ex, ($x$, 0, $\infty$))
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assert(tst==1)
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print("Test 05 passed")
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test05()
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‎web2/cadabra2/source/layout.html‎

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@@ -196,7 +196,7 @@
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</div>
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<div id="bottombar">
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<div id="bottomleft">Copyright &copy; 2001-2021 Kasper Peeters</div>
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<div id="bottomleft">Copyright &copy; 2001-2022 Kasper Peeters</div>
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<div id="bottomright">Questions? <a href="mailto:[email protected]">[email protected]</a></div>
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</div>
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