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Merge branch 'JuliaSymbolics:main' into main
2 parents 6bd7b60 + cbc02fd commit 721eece

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‎src/methods/risch/frontend.jl‎

Lines changed: 1 addition & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -661,8 +661,7 @@ Base.promote(x::MPolyRingElem{Nemo.QQBarFieldElem}, y::QQFieldElem) = promote(x,
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662662

663663

664-
function TowerOfDifferentialFields(terms::Vector{Term}) where
665-
{T<:FieldElement, P<:MPolyRingElem{T}, F<:FracElem{P}}
664+
function TowerOfDifferentialFields(terms::Vector{Term})
666665
n = length(terms)
667666
MF = parent(terms[1].arg)
668667
MR = base_ring(MF)

‎src/methods/rule_based/general.jl‎

Lines changed: 173 additions & 165 deletions
Original file line numberDiff line numberDiff line change
@@ -1,17 +1,15 @@
11
# ===== Special functions from a lot of packages
2-
# TODO extension to Symbolics?
3-
4-
# function from SpecialFunctions.jl that are not yet registered
5-
@register_symbolic SymbolicUtils.expinti(x)
6-
@register_symbolic SymbolicUtils.expint(nu, z)
7-
@register_symbolic SymbolicUtils.gamma(x, y)
8-
@register_symbolic SymbolicUtils.sinint(x)
9-
@register_symbolic SymbolicUtils.cosint(x)
10-
# other from SpecialFunctions.jl used:
11-
# SymbolicUtils.gamma(x)
12-
# SymbolicUtils.loggamma
13-
# SymbolicUtils.erfi
14-
# SymbolicUtils.erf
2+
3+
# function from SpecialFunctions.jl used:
4+
# SpecialFunctions.expinti(x)
5+
# SpecialFunctions.expint(nu, z)
6+
# SpecialFunctions.gamma(x, y)
7+
# SpecialFunctions.sinint(x)
8+
# SpecialFunctions.cosint(x)
9+
# SpecialFunctions.gamma(x)
10+
# SpecialFunctions.loggamma
11+
# SpecialFunctions.erfi
12+
# SpecialFunctions.erf
1513

1614
using Elliptic
1715
@register_symbolic Elliptic.F(phi, m) # incomplete first kind
@@ -27,9 +25,19 @@ elliptic_pi(nu, phi, m) = Elliptic.Pi(nu, phi, m)
2725
elliptic_pi(nu, m) = Elliptic.Pi(nu, π/2, m)
2826

2927
using HypergeometricFunctions
28+
"""
29+
Calculates the 2F1 Hypergeometric function using the HypergeometricFunctions.jl package,
30+
but also wraps the inputs in Complex numbers. so:
31+
hypergeometric2f1(a, b, c, z) = HypergeometricFunctions._₂F₁(Complex(a), Complex(b), Complex(c), Complex(z))
32+
"""
3033
hypergeometric2f1(a, b, c, z) = HypergeometricFunctions._₂F₁(Complex(a), Complex(b), Complex(c), Complex(z))
3134
@register_symbolic hypergeometric2f1(a, b, c, z)
3235

36+
"""
37+
Calculates the pFq Hypergeometric function using the HypergeometricFunctions.jl package,
38+
but also wraps the inputs in Complex numbers. so:
39+
hypergeometricpFq(a, b, z) = HypergeometricFunctions.pFq(a, b, Complex(z))
40+
"""
3341
hypergeometricpFq(a, b, z) = HypergeometricFunctions.pFq(a, b, Complex(z))
3442
@register_symbolic hypergeometricpFq(a::Vector, b::Vector, z)
3543

@@ -52,8 +60,8 @@ coshintegral(x::Any) = println("hyperbolic cosine integral Chi(z) function (http
5260
# ===== Global variables
5361
# symbolic functions
5462
# ∫(intgerand, intgeration variable)
55-
# subst is just for when integral inside the real subst function is not solved
56-
@syms ∫(var1,var2) subst(var1, var2, var3)
63+
# substitute_after_int is just for when integral inside the real substitute_after_int function is not solved
64+
@syms ∫(var1,var2) substitute_after_int(var1, var2, var3)
5765

5866
# very big arrays containing rules and their identifiers
5967
const RULES = SymbolicUtils.Rule[]
@@ -72,154 +80,154 @@ all_rules_paths = [
7280
"9 Miscellaneous/0.1 Integrand simplification rules.jl"
7381

7482
"1 Algebraic functions/1.1 Binomial products/1.1.1 Linear/1.1.1.1 (a+b x)^m.jl"
75-
"1 Algebraic functions/1.1 Binomial products/1.1.1 Linear/1.1.1.2 (a+b x)^m (c+d x)^n.jl"
76-
"1 Algebraic functions/1.1 Binomial products/1.1.1 Linear/1.1.1.3 (a+b x)^m (c+d x)^n (e+f x)^p.jl"
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"1 Algebraic functions/1.1 Binomial products/1.1.1 Linear/1.1.1.4 (a+b x)^m (c+d x)^n (e+f x)^p (g+h x)^q.jl"
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"1 Algebraic functions/1.1 Binomial products/1.1.2 Quadratic/1.1.2.1 (a+b x^2)^p.jl"
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"1 Algebraic functions/1.1 Binomial products/1.1.2 Quadratic/1.1.2.2 (c x)^m (a+b x^2)^p.jl"
81-
"1 Algebraic functions/1.1 Binomial products/1.1.2 Quadratic/1.1.2.3 (a+b x^2)^p (c+d x^2)^q.jl"
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"1 Algebraic functions/1.1 Binomial products/1.1.2 Quadratic/1.1.2.4 (e x)^m (a+b x^2)^p (c+d x^2)^q.jl"
83-
# 5, 6, 7, 8, 9
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"1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.1 (a+b x^n)^p.jl"
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"1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.2 (c x)^m (a+b x^n)^p.jl"
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"1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.3 (a+b x^n)^p (c+d x^n)^q.jl"
88-
"1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.4 (e x)^m (a+b x^n)^p (c+d x^n)^q.jl"
89-
"1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.5 (a+b x^n)^p (c+d x^n)^q (e+f x^n)^r.jl"
90-
"1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.6 (g x)^m (a+b x^n)^p (c+d x^n)^q (e+f x^n)^r.jl"
91-
92-
"1 Algebraic functions/1.2 Trinomial products/1.2.1 Quadratic/1.2.1.1 (a+b x+c x^2)^p.jl"
93-
"1 Algebraic functions/1.2 Trinomial products/1.2.1 Quadratic/1.2.1.2 (d+e x)^m (a+b x+c x^2)^p.jl"
94-
"1 Algebraic functions/1.2 Trinomial products/1.2.1 Quadratic/1.2.1.3 (d+e x)^m (f+g x) (a+b x+c x^2)^p.jl" # not most updated version?
95-
"1 Algebraic functions/1.2 Trinomial products/1.2.1 Quadratic/1.2.1.4 (d+e x)^m (f+g x)^n (a+b x+c x^2)^p.jl" # not most updated version?
96-
# 1.2.1.5
97-
98-
"1 Algebraic functions/1.2 Trinomial products/1.2.2 Quartic/1.2.2.1 (a+b x^2+c x^4)^p.jl"
99-
"1 Algebraic functions/1.2 Trinomial products/1.2.2 Quartic/1.2.2.2 (d x)^m (a+b x^2+c x^4)^p.jl"
100-
"1 Algebraic functions/1.2 Trinomial products/1.2.2 Quartic/1.2.2.3 (d+e x^2)^q (a+b x^2+c x^4)^p.jl"
101-
# 1.2.2.4
102-
103-
"1 Algebraic functions/1.2 Trinomial products/1.2.3 General/1.2.3.1 (a+b x^n+c x^(2 n))^p.jl"
104-
# 1.2.3.2, 1.2.3.3, 1.2.3.4
105-
106-
"1 Algebraic functions/1.1 Binomial products/1.1.4 Improper/1.1.4.1 (a x^j+b x^n)^p.jl"
107-
"1 Algebraic functions/1.1 Binomial products/1.1.4 Improper/1.1.4.2 (c x)^m (a x^j+b x^n)^p.jl"
108-
"1 Algebraic functions/1.1 Binomial products/1.1.4 Improper/1.1.4.3 (e x)^m (a x^j+b x^k)^p (c+d x^n)^q.jl"
109-
110-
# 1.2.4.1, 1.2.4.2, 1.2.4.3, 1.2.4.4
111-
112-
# 1.4.1, 1.4.2
113-
114-
"1 Algebraic functions/1.1 Binomial products/1.1.1 Linear/1.1.1.7 P(x) (a+b x)^m (c+d x)^n (e+f x)^p (g+h x)^q.jl"
115-
"1 Algebraic functions/1.1 Binomial products/1.1.1 Linear/1.1.1.6 P(x) (a+b x)^m (c+d x)^n (e+f x)^p.jl"
116-
"1 Algebraic functions/1.1 Binomial products/1.1.1 Linear/1.1.1.5 P(x) (a+b x)^m (c+d x)^n.jl"
117-
118-
"1 Algebraic functions/1.2 Trinomial products/1.2.2 Quartic/1.2.2.5 P(x) (a+b x^2+c x^4)^p.jl"
119-
"1 Algebraic functions/1.2 Trinomial products/1.2.2 Quartic/1.2.2.4 (f x)^m (d+e x^2)^q (a+b x^2+c x^4)^p.jl"
120-
121-
"1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.7 P(x) (a+b x^n)^p.jl"
122-
"1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.8 P(x) (c x)^m (a+b x^n)^p.jl"
123-
124-
# TODO 1.3.4 quale?
125-
126-
127-
128-
"2 Exponentials/2.1 (c+d x)^m (a+b (F^(g (e+f x)))^n)^p.jl"
129-
"2 Exponentials/2.2 (c+d x)^m (F^(g (e+f x)))^n (a+b (F^(g (e+f x)))^n)^p.jl"
130-
"2 Exponentials/2.3 Miscellaneous exponentials.jl"
131-
132-
133-
134-
135-
136-
137-
"3 Logarithms/3.1/3.1.1 (a+b log(c x^n))^p.jl"
138-
"3 Logarithms/3.1/3.1.2 (d x)^m (a+b log(c x^n))^p.jl"
139-
"3 Logarithms/3.1/3.1.3 (d+e x^r)^q (a+b log(c x^n))^p.jl"
140-
"3 Logarithms/3.1/3.1.4 (f x)^m (d+e x^r)^q (a+b log(c x^n))^p.jl"
141-
"3 Logarithms/3.1/3.1.5 u (a+b log(c x^n))^p.jl"
142-
"3 Logarithms/3.2/3.2.1 (f+g x)^m (A+B log(e ((a+b x) over (c+d x))^n))^p.jl"
143-
"3 Logarithms/3.2/3.2.2 (f+g x)^m (h+i x)^q (A+B log(e ((a+b x) over (c+d x))^n))^p.jl"
144-
"3 Logarithms/3.2/3.2.3 u log(e (f (a+b x)^p (c+d x)^q)^r)^s.jl"
145-
"3 Logarithms/3.3 u (a+b log(c (d+e x)^n))^p.jl"
146-
"3 Logarithms/3.4 u (a+b log(c (d+e x^m)^n))^p.jl"
147-
"3 Logarithms/3.5 Miscellaneous logarithms.jl"
148-
149-
150-
151-
152-
153-
"4 Trig functions/4.1 Sine/4.1.0/4.1.0.1 (a sin)^m (b trg)^n.jl"
154-
"4 Trig functions/4.1 Sine/4.1.0/4.1.0.2 (a trg)^m (b tan)^n.jl"
155-
"4 Trig functions/4.1 Sine/4.1.0/4.1.0.3 (a csc)^m (b sec)^n.jl"
156-
157-
"4 Trig functions/4.1 Sine/4.1.1/4.1.1.1 (a+b sin)^n.jl"
158-
"4 Trig functions/4.1 Sine/4.1.1/4.1.1.2 (g cos)^p (a+b sin)^m.jl"
159-
"4 Trig functions/4.1 Sine/4.1.1/4.1.1.3 (g tan)^p (a+b sin)^m.jl"
160-
161-
"4 Trig functions/4.1 Sine/4.1.2/4.1.2.1 (a+b sin)^m (c+d sin)^n.jl"
162-
"4 Trig functions/4.1 Sine/4.1.2/4.1.2.2 (g cos)^p (a+b sin)^m (c+d sin)^n.jl"
163-
"4 Trig functions/4.1 Sine/4.1.2/4.1.2.3 (g sin)^p (a+b sin)^m (c+d sin)^n.jl"
164-
165-
"4 Trig functions/4.1 Sine/4.1.3 (a+b sin)^m (c+d sin)^n (A+B sin).jl"
166-
167-
"4 Trig functions/4.1 Sine/4.1.4/4.1.4.1 (a+b sin)^m (A+B sin+C sin^2).jl"
168-
"4 Trig functions/4.1 Sine/4.1.4/4.1.4.2 (a+b sin)^m (c+d sin)^n (A+B sin+C sin^2).jl"
169-
170-
"4 Trig functions/4.1 Sine/4.1.5 trig^m (a cos+b sin)^n.jl"
171-
"4 Trig functions/4.1 Sine/4.1.6 (a+b cos+c sin)^n.jl"
172-
"4 Trig functions/4.1 Sine/4.1.7 (d trig)^m (a+b (c sin)^n)^p.jl"
173-
# 4.1.8
174-
"4 Trig functions/4.1 Sine/4.1.9 trig^m (a+b sin^n+c sin^(2 n))^p.jl"
175-
"4 Trig functions/4.1 Sine/4.1.10 (c+d x)^m (a+b sin)^n.jl"
176-
"4 Trig functions/4.1 Sine/4.1.11 (e x)^m (a+b x^n)^p sin.jl"
177-
"4 Trig functions/4.1 Sine/4.1.12 (e x)^m (a+b sin(c+d x^n))^p.jl"
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"4 Trig functions/4.1 Sine/4.1.13 (d+e x)^m sin(a+b x+c x^2)^n.jl"
179-
180-
"4 Trig functions/4.3 Tangent/4.3.1.1 (a+b tan)^n.jl"
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"4 Trig functions/4.3 Tangent/4.3.1.2 (d sec)^m (a+b tan)^n.jl"
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"4 Trig functions/4.3 Tangent/4.3.1.3 (d sin)^m (a+b tan)^n.jl"
183-
184-
"4 Trig functions/4.5 Secant/4.5.1.1 (a+b sec)^n.jl"
185-
"4 Trig functions/4.5 Secant/4.5.1.2 (d sec)^n (a+b sec)^m.jl"
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"4 Trig functions/4.5 Secant/4.5.1.3 (d sin)^n (a+b sec)^m.jl"
187-
"4 Trig functions/4.5 Secant/4.5.1.4 (d tan)^n (a+b sec)^m.jl"
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"4 Trig functions/4.5 Secant/4.5.7 (d trig)^m (a+b (c sec)^n)^p.jl"
189-
190-
"4 Trig functions/4.7 Miscellaneous/4.7.4 (c trig)^m (d trig)^n.jl"
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"4 Trig functions/4.7 Miscellaneous/4.7.7 F^(c (a+b x)) trig(d+e x)^n.jl"
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"5 Inverse trig functions/5.1 Inverse sine/5.1.1 (a+b arcsin(c x))^n.jl"
197-
"5 Inverse trig functions/5.1 Inverse sine/5.1.2 (d x)^m (a+b arcsin(c x))^n.jl"
198-
199-
"5 Inverse trig functions/5.3 Inverse tangent/5.3.1 (a+b arctan(c x^n))^p.jl"
200-
"5 Inverse trig functions/5.3 Inverse tangent/5.3.2 (d x)^m (a+b arctan(c x^n))^p.jl"
201-
202-
203-
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205-
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"7 Inverse hyperbolic functions/7.1 Inverse hyperbolic sine/7.1.1 (a+b arcsinh(c x))^n.jl"
209-
"7 Inverse hyperbolic functions/7.1 Inverse hyperbolic sine/7.1.2 (d x)^m (a+b arcsinh(c x))^n.jl"
210-
"7 Inverse hyperbolic functions/7.1 Inverse hyperbolic sine/7.1.3 (d+e x^2)^p (a+b arcsinh(c x))^n.jl"
211-
"7 Inverse hyperbolic functions/7.1 Inverse hyperbolic sine/7.1.4 (f x)^m (d+e x^2)^p (a+b arcsinh(c x))^n.jl"
212-
"7 Inverse hyperbolic functions/7.1 Inverse hyperbolic sine/7.1.5 u (a+b arcsinh(c x))^n.jl"
213-
"7 Inverse hyperbolic functions/7.1 Inverse hyperbolic sine/7.1.6 Miscellaneous inverse hyperbolic sine.jl"
214-
215-
"7 Inverse hyperbolic functions/7.2 Inverse hyperbolic cosine/7.2.1 (a+b arccosh(c x))^n.jl"
216-
"7 Inverse hyperbolic functions/7.2 Inverse hyperbolic cosine/7.2.2 (d x)^m (a+b arccosh(c x))^n.jl"
217-
"7 Inverse hyperbolic functions/7.2 Inverse hyperbolic cosine/7.2.3 (d+e x^2)^p (a+b arccosh(c x))^n.jl"
218-
"7 Inverse hyperbolic functions/7.2 Inverse hyperbolic cosine/7.2.4 (f x)^m (d+e x^2)^p (a+b arccosh(c x))^n.jl"
219-
"7 Inverse hyperbolic functions/7.2 Inverse hyperbolic cosine/7.2.5 u (a+b arccosh(c x))^n.jl"
220-
"7 Inverse hyperbolic functions/7.2 Inverse hyperbolic cosine/7.2.6 Miscellaneous inverse hyperbolic cosine.jl"
221-
222-
"7 Inverse hyperbolic functions/7.3 Inverse hyperbolic tangent/7.3.1 (a+b arctanh(c x^n))^p.jl"
223-
"7 Inverse hyperbolic functions/7.3 Inverse hyperbolic tangent/7.3.2 (d x)^m (a+b arctanh(c x^n))^p.jl"
224-
"7 Inverse hyperbolic functions/7.3 Inverse hyperbolic tangent/7.3.3 (d+e x)^m (a+b arctanh(c x^n))^p.jl"
83+
# "1 Algebraic functions/1.1 Binomial products/1.1.1 Linear/1.1.1.2 (a+b x)^m (c+d x)^n.jl"
84+
# "1 Algebraic functions/1.1 Binomial products/1.1.1 Linear/1.1.1.3 (a+b x)^m (c+d x)^n (e+f x)^p.jl"
85+
# "1 Algebraic functions/1.1 Binomial products/1.1.1 Linear/1.1.1.4 (a+b x)^m (c+d x)^n (e+f x)^p (g+h x)^q.jl"
86+
#
87+
# "1 Algebraic functions/1.1 Binomial products/1.1.2 Quadratic/1.1.2.1 (a+b x^2)^p.jl"
88+
# "1 Algebraic functions/1.1 Binomial products/1.1.2 Quadratic/1.1.2.2 (c x)^m (a+b x^2)^p.jl"
89+
# "1 Algebraic functions/1.1 Binomial products/1.1.2 Quadratic/1.1.2.3 (a+b x^2)^p (c+d x^2)^q.jl"
90+
# "1 Algebraic functions/1.1 Binomial products/1.1.2 Quadratic/1.1.2.4 (e x)^m (a+b x^2)^p (c+d x^2)^q.jl"
91+
# # 5, 6, 7, 8, 9
92+
#
93+
# "1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.1 (a+b x^n)^p.jl"
94+
# "1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.2 (c x)^m (a+b x^n)^p.jl"
95+
# "1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.3 (a+b x^n)^p (c+d x^n)^q.jl"
96+
# "1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.4 (e x)^m (a+b x^n)^p (c+d x^n)^q.jl"
97+
# "1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.5 (a+b x^n)^p (c+d x^n)^q (e+f x^n)^r.jl"
98+
# "1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.6 (g x)^m (a+b x^n)^p (c+d x^n)^q (e+f x^n)^r.jl"
99+
#
100+
# "1 Algebraic functions/1.2 Trinomial products/1.2.1 Quadratic/1.2.1.1 (a+b x+c x^2)^p.jl"
101+
# "1 Algebraic functions/1.2 Trinomial products/1.2.1 Quadratic/1.2.1.2 (d+e x)^m (a+b x+c x^2)^p.jl"
102+
# "1 Algebraic functions/1.2 Trinomial products/1.2.1 Quadratic/1.2.1.3 (d+e x)^m (f+g x) (a+b x+c x^2)^p.jl" # not most updated version?
103+
# "1 Algebraic functions/1.2 Trinomial products/1.2.1 Quadratic/1.2.1.4 (d+e x)^m (f+g x)^n (a+b x+c x^2)^p.jl" # not most updated version?
104+
# # 1.2.1.5
105+
#
106+
# "1 Algebraic functions/1.2 Trinomial products/1.2.2 Quartic/1.2.2.1 (a+b x^2+c x^4)^p.jl"
107+
# "1 Algebraic functions/1.2 Trinomial products/1.2.2 Quartic/1.2.2.2 (d x)^m (a+b x^2+c x^4)^p.jl"
108+
# "1 Algebraic functions/1.2 Trinomial products/1.2.2 Quartic/1.2.2.3 (d+e x^2)^q (a+b x^2+c x^4)^p.jl"
109+
# # 1.2.2.4
110+
#
111+
# "1 Algebraic functions/1.2 Trinomial products/1.2.3 General/1.2.3.1 (a+b x^n+c x^(2 n))^p.jl"
112+
# # 1.2.3.2, 1.2.3.3, 1.2.3.4
113+
#
114+
# "1 Algebraic functions/1.1 Binomial products/1.1.4 Improper/1.1.4.1 (a x^j+b x^n)^p.jl"
115+
# "1 Algebraic functions/1.1 Binomial products/1.1.4 Improper/1.1.4.2 (c x)^m (a x^j+b x^n)^p.jl"
116+
# "1 Algebraic functions/1.1 Binomial products/1.1.4 Improper/1.1.4.3 (e x)^m (a x^j+b x^k)^p (c+d x^n)^q.jl"
117+
#
118+
# # 1.2.4.1, 1.2.4.2, 1.2.4.3, 1.2.4.4
119+
#
120+
# # 1.4.1, 1.4.2
121+
#
122+
# "1 Algebraic functions/1.1 Binomial products/1.1.1 Linear/1.1.1.7 P(x) (a+b x)^m (c+d x)^n (e+f x)^p (g+h x)^q.jl"
123+
# "1 Algebraic functions/1.1 Binomial products/1.1.1 Linear/1.1.1.6 P(x) (a+b x)^m (c+d x)^n (e+f x)^p.jl"
124+
# "1 Algebraic functions/1.1 Binomial products/1.1.1 Linear/1.1.1.5 P(x) (a+b x)^m (c+d x)^n.jl"
125+
#
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# "1 Algebraic functions/1.2 Trinomial products/1.2.2 Quartic/1.2.2.5 P(x) (a+b x^2+c x^4)^p.jl"
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# "1 Algebraic functions/1.2 Trinomial products/1.2.2 Quartic/1.2.2.4 (f x)^m (d+e x^2)^q (a+b x^2+c x^4)^p.jl"
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#
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# "1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.7 P(x) (a+b x^n)^p.jl"
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# "1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.8 P(x) (c x)^m (a+b x^n)^p.jl"
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#
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# # TODO 1.3.4 quale?
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#
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#
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#
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# "2 Exponentials/2.1 (c+d x)^m (a+b (F^(g (e+f x)))^n)^p.jl"
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# "2 Exponentials/2.2 (c+d x)^m (F^(g (e+f x)))^n (a+b (F^(g (e+f x)))^n)^p.jl"
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# "2 Exponentials/2.3 Miscellaneous exponentials.jl"
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#
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#
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#
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#
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#
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#
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# "3 Logarithms/3.1/3.1.1 (a+b log(c x^n))^p.jl"
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# "3 Logarithms/3.1/3.1.2 (d x)^m (a+b log(c x^n))^p.jl"
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# "3 Logarithms/3.1/3.1.3 (d+e x^r)^q (a+b log(c x^n))^p.jl"
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# "3 Logarithms/3.1/3.1.4 (f x)^m (d+e x^r)^q (a+b log(c x^n))^p.jl"
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# "3 Logarithms/3.1/3.1.5 u (a+b log(c x^n))^p.jl"
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# "3 Logarithms/3.2/3.2.1 (f+g x)^m (A+B log(e ((a+b x) over (c+d x))^n))^p.jl"
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# "3 Logarithms/3.2/3.2.2 (f+g x)^m (h+i x)^q (A+B log(e ((a+b x) over (c+d x))^n))^p.jl"
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# "3 Logarithms/3.2/3.2.3 u log(e (f (a+b x)^p (c+d x)^q)^r)^s.jl"
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# "3 Logarithms/3.3 u (a+b log(c (d+e x)^n))^p.jl"
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# "3 Logarithms/3.4 u (a+b log(c (d+e x^m)^n))^p.jl"
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# "3 Logarithms/3.5 Miscellaneous logarithms.jl"
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#
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#
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#
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#
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#
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# "4 Trig functions/4.1 Sine/4.1.0/4.1.0.1 (a sin)^m (b trg)^n.jl"
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# "4 Trig functions/4.1 Sine/4.1.0/4.1.0.2 (a trg)^m (b tan)^n.jl"
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# "4 Trig functions/4.1 Sine/4.1.0/4.1.0.3 (a csc)^m (b sec)^n.jl"
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#
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# "4 Trig functions/4.1 Sine/4.1.1/4.1.1.1 (a+b sin)^n.jl"
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# "4 Trig functions/4.1 Sine/4.1.1/4.1.1.2 (g cos)^p (a+b sin)^m.jl"
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# "4 Trig functions/4.1 Sine/4.1.1/4.1.1.3 (g tan)^p (a+b sin)^m.jl"
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#
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# "4 Trig functions/4.1 Sine/4.1.2/4.1.2.1 (a+b sin)^m (c+d sin)^n.jl"
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# "4 Trig functions/4.1 Sine/4.1.2/4.1.2.2 (g cos)^p (a+b sin)^m (c+d sin)^n.jl"
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# "4 Trig functions/4.1 Sine/4.1.2/4.1.2.3 (g sin)^p (a+b sin)^m (c+d sin)^n.jl"
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#
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# "4 Trig functions/4.1 Sine/4.1.3 (a+b sin)^m (c+d sin)^n (A+B sin).jl"
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#
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# "4 Trig functions/4.1 Sine/4.1.4/4.1.4.1 (a+b sin)^m (A+B sin+C sin^2).jl"
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# "4 Trig functions/4.1 Sine/4.1.4/4.1.4.2 (a+b sin)^m (c+d sin)^n (A+B sin+C sin^2).jl"
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#
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# "4 Trig functions/4.1 Sine/4.1.5 trig^m (a cos+b sin)^n.jl"
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# "4 Trig functions/4.1 Sine/4.1.6 (a+b cos+c sin)^n.jl"
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# "4 Trig functions/4.1 Sine/4.1.7 (d trig)^m (a+b (c sin)^n)^p.jl"
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# # 4.1.8
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# "4 Trig functions/4.1 Sine/4.1.9 trig^m (a+b sin^n+c sin^(2 n))^p.jl"
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# "4 Trig functions/4.1 Sine/4.1.10 (c+d x)^m (a+b sin)^n.jl"
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# "4 Trig functions/4.1 Sine/4.1.11 (e x)^m (a+b x^n)^p sin.jl"
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# "4 Trig functions/4.1 Sine/4.1.12 (e x)^m (a+b sin(c+d x^n))^p.jl"
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# "4 Trig functions/4.1 Sine/4.1.13 (d+e x)^m sin(a+b x+c x^2)^n.jl"
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#
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# "4 Trig functions/4.3 Tangent/4.3.1.1 (a+b tan)^n.jl"
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# "4 Trig functions/4.3 Tangent/4.3.1.2 (d sec)^m (a+b tan)^n.jl"
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# "4 Trig functions/4.3 Tangent/4.3.1.3 (d sin)^m (a+b tan)^n.jl"
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#
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# "4 Trig functions/4.5 Secant/4.5.1.1 (a+b sec)^n.jl"
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# "4 Trig functions/4.5 Secant/4.5.1.2 (d sec)^n (a+b sec)^m.jl"
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# "4 Trig functions/4.5 Secant/4.5.1.3 (d sin)^n (a+b sec)^m.jl"
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# "4 Trig functions/4.5 Secant/4.5.1.4 (d tan)^n (a+b sec)^m.jl"
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# "4 Trig functions/4.5 Secant/4.5.7 (d trig)^m (a+b (c sec)^n)^p.jl"
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#
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# "4 Trig functions/4.7 Miscellaneous/4.7.4 (c trig)^m (d trig)^n.jl"
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# "4 Trig functions/4.7 Miscellaneous/4.7.7 F^(c (a+b x)) trig(d+e x)^n.jl"
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#
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#
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#
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#
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# "5 Inverse trig functions/5.1 Inverse sine/5.1.1 (a+b arcsin(c x))^n.jl"
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# "5 Inverse trig functions/5.1 Inverse sine/5.1.2 (d x)^m (a+b arcsin(c x))^n.jl"
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#
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# "5 Inverse trig functions/5.3 Inverse tangent/5.3.1 (a+b arctan(c x^n))^p.jl"
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# "5 Inverse trig functions/5.3 Inverse tangent/5.3.2 (d x)^m (a+b arctan(c x^n))^p.jl"
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#
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#
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#
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#
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#
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#
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#
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# "7 Inverse hyperbolic functions/7.1 Inverse hyperbolic sine/7.1.1 (a+b arcsinh(c x))^n.jl"
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# "7 Inverse hyperbolic functions/7.1 Inverse hyperbolic sine/7.1.2 (d x)^m (a+b arcsinh(c x))^n.jl"
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# "7 Inverse hyperbolic functions/7.1 Inverse hyperbolic sine/7.1.3 (d+e x^2)^p (a+b arcsinh(c x))^n.jl"
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# "7 Inverse hyperbolic functions/7.1 Inverse hyperbolic sine/7.1.4 (f x)^m (d+e x^2)^p (a+b arcsinh(c x))^n.jl"
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# "7 Inverse hyperbolic functions/7.1 Inverse hyperbolic sine/7.1.5 u (a+b arcsinh(c x))^n.jl"
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# "7 Inverse hyperbolic functions/7.1 Inverse hyperbolic sine/7.1.6 Miscellaneous inverse hyperbolic sine.jl"
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#
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# "7 Inverse hyperbolic functions/7.2 Inverse hyperbolic cosine/7.2.1 (a+b arccosh(c x))^n.jl"
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# "7 Inverse hyperbolic functions/7.2 Inverse hyperbolic cosine/7.2.2 (d x)^m (a+b arccosh(c x))^n.jl"
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# "7 Inverse hyperbolic functions/7.2 Inverse hyperbolic cosine/7.2.3 (d+e x^2)^p (a+b arccosh(c x))^n.jl"
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# "7 Inverse hyperbolic functions/7.2 Inverse hyperbolic cosine/7.2.4 (f x)^m (d+e x^2)^p (a+b arccosh(c x))^n.jl"
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# "7 Inverse hyperbolic functions/7.2 Inverse hyperbolic cosine/7.2.5 u (a+b arccosh(c x))^n.jl"
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# "7 Inverse hyperbolic functions/7.2 Inverse hyperbolic cosine/7.2.6 Miscellaneous inverse hyperbolic cosine.jl"
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#
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# "7 Inverse hyperbolic functions/7.3 Inverse hyperbolic tangent/7.3.1 (a+b arctanh(c x^n))^p.jl"
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# "7 Inverse hyperbolic functions/7.3 Inverse hyperbolic tangent/7.3.2 (d x)^m (a+b arctanh(c x^n))^p.jl"
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# "7 Inverse hyperbolic functions/7.3 Inverse hyperbolic tangent/7.3.3 (d+e x)^m (a+b arctanh(c x^n))^p.jl"
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]

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