diff options
Diffstat (limited to 'macros/luatex/latex/luacas/tex/test/calculus')
| -rw-r--r-- | macros/luatex/latex/luacas/tex/test/calculus/derivatives.lua | 30 | ||||
| -rw-r--r-- | macros/luatex/latex/luacas/tex/test/calculus/integrals.lua | 54 |
2 files changed, 84 insertions, 0 deletions
diff --git a/macros/luatex/latex/luacas/tex/test/calculus/derivatives.lua b/macros/luatex/latex/luacas/tex/test/calculus/derivatives.lua new file mode 100644 index 0000000000..5d5429f59b --- /dev/null +++ b/macros/luatex/latex/luacas/tex/test/calculus/derivatives.lua @@ -0,0 +1,30 @@ +local a = DD(SymbolExpression("x") * SymbolExpression("y"), SymbolExpression("x")) +local b = DD(Integer(3) * SymbolExpression("x") ^ Integer(2) + Integer(2) * SymbolExpression("x") + Integer(6), SymbolExpression("x")) +local c = DD(E ^ SymbolExpression("x"), SymbolExpression("x")) +local d = DD(FunctionExpression("f", {SymbolExpression("x") ^ Integer(2)})) +local e = DD(SymbolExpression("x") ^ SymbolExpression("x")) +local f = DD(PolynomialRing({Integer(3), Integer(4), Integer(5)}, "x")) +local g = DD(LN(SymbolExpression("y")), SymbolExpression("y")) +local h = DD(SymbolExpression("x") ^ SymbolExpression("n")) +local i = DD(SIN((SymbolExpression("x")))) +local j = DD(SIN(Integer(2) * COS(SymbolExpression("x")))) +local k = DD(ARCTAN(SymbolExpression("x") ^ (Integer(1) / Integer(2)))) +local l = DD(ARCSEC(SymbolExpression("x"))) + +starttest("derivatives") + +testeq(a, dparse("DD(x*y, x)")) +testeq(a:autosimplify(), parse("y"), a) +testeq(b:autosimplify(), parse("6 * x + 2"), b) +testeq(c:autosimplify(), parse("e^x"), c) +testeq(d:autosimplify(), (Integer(2) * SymbolExpression("x") * FunctionExpression("f", {SymbolExpression("x")^Integer(2)}, {Integer(1)})):autosimplify(), d) +testeq(e:autosimplify(), parse("x^x * (1 + ln(x))"), e) +testeq(f:autosimplify(), parse("4 + 10 * x"), f) +testeq(g:autosimplify(), parse("y ^ -1"), g) +testeq(h:autosimplify(), parse("n * x ^ (-1 + n)"), h) +testeq(i:autosimplify(), parse("cos(x)"), i) +testeq(j:autosimplify(), parse("-2 * cos(2 * cos(x)) * sin(x)"), j) +testeq(k:autosimplify(), parse("1/2 * x^(-1/2) * (1+x) ^ -1"), k) +testeq(l:autosimplify(), parse("abs(x)^-1 * (1 + -(x^2))^ (-1/2)"), l) + +endtest()
\ No newline at end of file diff --git a/macros/luatex/latex/luacas/tex/test/calculus/integrals.lua b/macros/luatex/latex/luacas/tex/test/calculus/integrals.lua new file mode 100644 index 0000000000..0c12f7a787 --- /dev/null +++ b/macros/luatex/latex/luacas/tex/test/calculus/integrals.lua @@ -0,0 +1,54 @@ +local a = dparse("int(x^2, x)") +local b = dparse("int(x^-1, x, 1, e)") +local c = dparse("int(3*x^2+2*x+6, x)") +local d = dparse("int(sin(x)*cos(x), x)") +local e = dparse("int(2*x*cos(x^2), x)") +local f = dparse("int(sin(2*x), x)") +local g = dparse("int(e^sin(x), x)") +local h = dparse("int((1 / (1 + (1 / x))), x)") +local i = dparse("int(e^(x^(1/2)), x)") +local j = dparse("int((x^3+1)/(x-2), x)") +local k = dparse("int((x^2-x+1)/(x^3+3*x^2+3*x+1), x)") +local l = dparse("int(1 / (x^3+6*x), x)") +local m = dparse("int(1/(x^2+x+1), x)") +local n = dparse("int(1/(x^3+2*x+2), x, 0, 1)") + +local o = dparse("int(x^2*e^x, x)") +local p = dparse("int((x^2+6*x+3)*sin(x), x)") +local q = dparse("int(x*e^x*sin(x),x)") +local r = dparse("int(cos(x)^3, x)") +local s = dparse("int(1/(e^x+1), x)") +local t = dparse("int(e^(2*x)*cos(3*x), x)") +local u = dparse("int((x^2-1)^2, x, -1, 1)") + +starttest("integration") +testeq(a, dparse("int(x ^ 2, x)")) +testeq(a:autosimplify(), parse("x^3/3"), a) +testeq(b:autosimplify(), parse("1"), b) +testeq(c:autosimplify(), parse("x^3+x^2+6*x"), c) +testeq(d:autosimplify(), parse("(-1/2 * (cos(x) ^ 2))"), d) +testeq(e:autosimplify(), parse("sin((x ^ 2))"), e) +testeq(f:autosimplify(), parse("(-1/2 * cos((2 * x)))"), f) +-- testeq(g:autosimplify(), dparse("int(e ^ (sin(x)), x)"), g) +testeq(h:autosimplify(), parse("x + (-1 * (log(e, 1 + (x ^ -1)))) + (-1 * (log(e, x)))"), h) +testeq(i:autosimplify(), parse("-2 * (e ^ (x ^ (1/2))) + 2 * (e ^ (x ^ (1/2))) * (x ^ (1/2))"), i) +testeq(j:autosimplify(), parse("((4 * x) + (x ^ 2) + (1/3 * (x ^ 3)) + (9 * log(e, (-2 + x))))"), j) +testeq(k:autosimplify(), parse("((-3/2 * ((1 + x) ^ -2)) + (3 * ((1 + x) ^ -1)) + log(e, (1 + x)))"), k) +testeq(l:autosimplify(), parse("((1/6 * log(e, x)) + (-1/12 * log(e, (6 + (x ^ 2)))))"), l) +testeq(m:autosimplify(), parse("2/3 * (3 ^ (1/2)) * (arctan((3 ^ (1/2)) * (1/3 + (2/3 * x))))"), m) +-- test(n:autosimplify(), [[((((6 * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + (1/420 * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3))) +-- * log(e, (18 * (((-6 * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + (-1/420 * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3))) ^ 2) * (((-18 * ((-264600 + (1/2 +-- * (216040608000 ^ 1/2))) ^ -1/3)) + (-1/140 * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3)) + (12 * (((-6 * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + (-1/420 * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3))) ^ 2))) ^ -1)))) + (((6 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ -1) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + ((-1/840 + (1/840 * (-3 ^ 1/2))) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3))) * log(e, (18 * (((-6 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ -1) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + ((1/840 + (-1/840 * (-3 ^ 1/2))) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3))) ^ 2) * (((-18 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ -1) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + ((1/280 + (-1/280 * (-3 ^ 1/2))) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3)) + (12 * (((-6 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ -1) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + ((1/840 + (-1/840 * (-3 ^ 1/2))) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3))) ^ 2))) ^ -1)))) + (((6 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ -2) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + (1/420 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ 2) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3))) * log(e, (18 * (((-6 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ -2) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + (-1/420 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ 2) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3))) ^ 2) * (((-18 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ -2) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + (-1/140 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ 2) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3)) + (12 * (((-6 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ -2) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + (-1/420 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ 2) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3))) ^ 2))) ^ -1)))) + (((-6 * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + (-1/420 * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3))) * log(e, (1 + (18 * (((-6 * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + (-1/420 * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3))) ^ 2) * (((-18 * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + (-1/140 * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3)) + (12 * (((-6 * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + (-1/420 * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3))) ^ 2))) ^ -1))))) + (((-6 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ -1) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + ((1/840 + (-1/840 * (-3 ^ 1/2))) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3))) * log(e, (1 + (18 * (((-6 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ -1) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + ((1/840 + (-1/840 * (-3 ^ 1/2))) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3))) ^ 2) * (((-18 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ -1) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + ((1/280 + (-1/280 * (-3 ^ 1/2))) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3)) + (12 * (((-6 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ -1) * ((-264600 + (1/2 * (216040608000 +-- ^ 1/2))) ^ -1/3)) + ((1/840 + (-1/840 * (-3 ^ 1/2))) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3))) ^ 2))) ^ -1))))) + (((-6 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ -2) * +-- ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + (-1/420 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ 2) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3))) * log(e, (1 + (18 * +-- (((-6 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ -2) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + (-1/420 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ 2) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3))) ^ 2) * (((-18 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ -2) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + (-1/140 * ((-1/2 + (1/2 * (-3 ^ 1/2))) +-- ^ 2) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3)) + (12 * (((-6 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ -2) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ -1/3)) + (-1/420 * ((-1/2 + (1/2 * (-3 ^ 1/2))) ^ 2) * ((-264600 + (1/2 * (216040608000 ^ 1/2))) ^ 1/3))) ^ 2))) ^ -1))))))]], n) + +testeq(o:autosimplify(), parse("((2 * (e ^ x)) + (-2 * (e ^ x) * x) + ((e ^ x) * (x ^ 2)))"), o) +testeq(p:autosimplify(), parse("((2 * cos(x)) + ((-3 + (-6 * x) + (-1 * (x ^ 2))) * cos(x)) + ((6 + (2 * x)) * sin(x)))"), p) +testeq(q:autosimplify(), parse("(1/2 * (e ^ x) * (cos(x))) + (-1/2 * (e ^ x) * x * (cos(x))) + (1/2 * (e ^ x) * x * (sin(x)))"), q) +testeq(r:autosimplify(), parse("((3/4 * sin(x)) + (1/12 * sin((3 * x))))"), r) +testeq(s:autosimplify(), parse("log(e, 1 + (-1 * ((1 + (e ^ x)) ^ -1)))"), s) +testeq(t:autosimplify(), parse("(2/13 * (e ^ (2 * x)) * (cos(3 * x))) + (3/13 * (e ^ (2 * x)) * (sin(3 * x)))"), t) +testeq(u:autosimplify(), parse("16/15"), u) +endtest() |