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Format code with JuliaFormatter v2.1.5
Applied JuliaFormatter to ensure consistent code formatting across the codebase. This includes formatting improvements to source files for better readability and consistency. 🤖 Generated with [Claude Code](https://claude.ai/code) Co-Authored-By: Claude <[email protected]>
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-35
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3 files changed

+58
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‎src/homotopy.jl‎

Lines changed: 13 additions & 7 deletions
Original file line numberDiff line numberDiff line change
@@ -132,8 +132,10 @@ partial_int_rules = [
132132
@rule 𝛷(~x, sech(~u)) => (atan(sinh(~u)), ~u)
133133
@rule 𝛷(~x, coth(~u)) => (log(sinh(~u)), ~u)
134134
# 1/trigonometric functions
135-
@rule 𝛷(~x, 1 / sin(~u)) => (log(csc(~u) + cot(~u)) + log(sin(~u)), ~u)
136-
@rule 𝛷(~x, 1 / cos(~u)) => (log(sec(~u) + tan(~u)) + log(cos(~u)), ~u)
135+
@rule 𝛷(~x, 1 /
136+
sin(~u)) => (log(csc(~u) + cot(~u)) + log(sin(~u)), ~u)
137+
@rule 𝛷(~x, 1 /
138+
cos(~u)) => (log(sec(~u) + tan(~u)) + log(cos(~u)), ~u)
137139
@rule 𝛷(~x, 1 / tan(~u)) => (log(sin(~u)) + log(tan(~u)), ~u)
138140
@rule 𝛷(~x, 1 / csc(~u)) => (cos(~u) + log(csc(~u)), ~u)
139141
@rule 𝛷(~x, 1 / sec(~u)) => (sin(~u) + log(sec(~u)), ~u)
@@ -160,7 +162,8 @@ partial_int_rules = [
160162
@rule 𝛷(~x, asech(~u)) => (asech(~u), ~u)
161163
@rule 𝛷(~x, acoth(~u)) => (~u * acot(~u) + log(~u + 1), ~u)
162164
# logarithmic and exponential functions
163-
@rule 𝛷(~x, log(~u)) => (
165+
@rule 𝛷(~x,
166+
log(~u)) => (
164167
~u + ~u * log(~u) +
165168
sum(pow_minus_rule(~u, ~x, -1); init = one(~u)),
166169
~u)
@@ -172,16 +175,19 @@ partial_int_rules = [
172175
sum(sqrt_rule(~u, ~x, ~k); init = one(~u)), ~u)
173176
@rule 𝛷(~x, sqrt(~u)) => (
174177
sum(sqrt_rule(~u, ~x, 0.5); init = one(~u)), ~u)
175-
@rule 𝛷(~x, 1 / sqrt(~u)) => (
178+
@rule 𝛷(~x, 1 /
179+
sqrt(~u)) => (
176180
sum(sqrt_rule(~u, ~x, -0.5); init = one(~u)), ~u)
177181
# rational functions
178-
@rule 𝛷(~x, 1 / ^(~u::is_univar_poly, ~k::is_pos_int)) => (
182+
@rule 𝛷(~x,
183+
1 / ^(~u::is_univar_poly, ~k::is_pos_int)) => (
179184
sum(pow_minus_rule(~u,
180185
~x,
181186
-~k);
182187
init = one(~u)),
183188
~u)
184-
@rule 𝛷(~x, 1 / ~u::is_univar_poly) => (
189+
@rule 𝛷(
190+
~x, 1 / ~u::is_univar_poly) => (
185191
sum(pow_minus_rule(~u, ~x, -1); init = one(~u)),
186192
~u)
187193
@rule 𝛷(~x, ^(~u, -1)) => (log(~u) + ~u * log(~u), ~u)
@@ -239,7 +245,7 @@ function pow_minus_rule(p, x, k; abstol = 1e-8)
239245
end
240246

241247
function sqrt_rule(p, x, k)
242-
h = Any[p^k, p^(k + 1)]
248+
h = Any[p ^ k, p ^ (k + 1)]
243249

244250
Δ = diff(p, x)
245251
push!(h, log(Δ / 2 + sqrt(p)))

‎src/integral.jl‎

Lines changed: 8 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -99,7 +99,8 @@ function integrate(eq, x = nothing;
9999

100100
plan = NumericalPlan(abstol, radius, complex_plane, opt)
101101

102-
s, u, ε = integrate_sum(eq, x; plan, bypass, num_trials, num_steps,
102+
s, u,
103+
ε = integrate_sum(eq, x; plan, bypass, num_trials, num_steps,
103104
show_basis, symbolic, max_basis, verbose, use_optim)
104105

105106
s = beautify(s)
@@ -206,7 +207,12 @@ end
206207
# in a future version
207208
function integrate_term(eq, x; kwargs...)
208209
args = Dict(kwargs)
209-
plan, num_steps, num_trials, show_basis, symbolic, verbose, max_basis = args[:plan],
210+
plan, num_steps,
211+
num_trials,
212+
show_basis,
213+
symbolic,
214+
verbose,
215+
max_basis = args[:plan],
210216
args[:num_steps], args[:num_trials], args[:show_basis],
211217
args[:symbolic], args[:verbose], args[:max_basis]
212218

‎src/rules.jl‎

Lines changed: 37 additions & 26 deletions
Original file line numberDiff line numberDiff line change
@@ -109,22 +109,28 @@ trigs_rules = [@rule tan(~x) => sin(~x) / cos(~x)
109109
@rule sec(~x) => one(~x) / cos(~x)
110110
@rule csc(~x) => one(~x) / sin(~x)
111111
@rule cot(~x) => cos(~x) / sin(~x)
112-
@rule sin(~n::is_int_gt_one * ~x) => sin((~n - 1) * ~x) * cos(~x) +
113-
cos((~n - 1) * ~x) * sin(~x)
114-
@rule cos(~n::is_int_gt_one * ~x) => cos((~n - 1) * ~x) * cos(~x) -
115-
sin((~n - 1) * ~x) * sin(~x)
116-
@rule tan(~n::is_int_gt_one * ~x) => (tan((~n - 1) * ~x) + tan(~x)) /
117-
(1 - tan((~n - 1) * ~x) * tan(~x))
118-
@rule csc(~n::is_int_gt_one * ~x) => sec((~n - 1) * ~x) * sec(~x) *
119-
csc((~n - 1) * ~x) * csc(~x) /
120-
(sec((~n - 1) * ~x) * csc(~x) +
121-
csc((~n - 1) * ~x) * sec(~x))
122-
@rule sec(~n::is_int_gt_one * ~x) => sec((~n - 1) * ~x) * sec(~x) *
123-
csc((~n - 1) * ~x) * csc(~x) /
124-
(csc((~n - 1) * ~x) * csc(~x) -
125-
sec((~n - 1) * ~x) * sec(~x))
126-
@rule cot(~n::is_int_gt_one * ~x) => (cot((~n - 1) * ~x) * cot(~x) - 1) /
127-
(cot((~n - 1) * ~x) + cot(~x))
112+
@rule sin(~n::is_int_gt_one *
113+
~x) => sin((~n - 1) * ~x) * cos(~x) +
114+
cos((~n - 1) * ~x) * sin(~x)
115+
@rule cos(~n::is_int_gt_one *
116+
~x) => cos((~n - 1) * ~x) * cos(~x) -
117+
sin((~n - 1) * ~x) * sin(~x)
118+
@rule tan(~n::is_int_gt_one *
119+
~x) => (tan((~n - 1) * ~x) + tan(~x)) /
120+
(1 - tan((~n - 1) * ~x) * tan(~x))
121+
@rule csc(~n::is_int_gt_one *
122+
~x) => sec((~n - 1) * ~x) * sec(~x) *
123+
csc((~n - 1) * ~x) * csc(~x) /
124+
(sec((~n - 1) * ~x) * csc(~x) +
125+
csc((~n - 1) * ~x) * sec(~x))
126+
@rule sec(~n::is_int_gt_one *
127+
~x) => sec((~n - 1) * ~x) * sec(~x) *
128+
csc((~n - 1) * ~x) * csc(~x) /
129+
(csc((~n - 1) * ~x) * csc(~x) -
130+
sec((~n - 1) * ~x) * sec(~x))
131+
@rule cot(~n::is_int_gt_one *
132+
~x) => (cot((~n - 1) * ~x) * cot(~x) - 1) /
133+
(cot((~n - 1) * ~x) + cot(~x))
128134
@rule 1 / sin(~x) => csc(~x)
129135
@rule 1 / cos(~x) => sec(~x)
130136
@rule 1 / tan(~x) => cot(~x)
@@ -140,18 +146,22 @@ trigs_rules = [@rule tan(~x) => sin(~x) / cos(~x)
140146
@rule sin(~x + ~y) => sin(~x) * cos(~y) + cos(~x) * sin(~y)
141147
@rule cos(~x + ~y) => cos(~x) * cos(~y) - sin(~x) * sin(~y)
142148
@rule tan(~x + ~y) => (tan(~x) + tan(~y)) / (1 - tan(~x) * tan(~y))
143-
@rule csc(~x + ~y) => sec(~x) * sec(~y) * csc(~x) * csc(~y) /
144-
(sec(~x) * csc(~y) + csc(~x) * sec(~y))
145-
@rule sec(~x + ~y) => sec(~x) * sec(~y) * csc(~x) * csc(~y) /
146-
(csc(~x) * csc(~y) - sec(~x) * sec(~y))
149+
@rule csc(~x +
150+
~y) => sec(~x) * sec(~y) * csc(~x) * csc(~y) /
151+
(sec(~x) * csc(~y) + csc(~x) * sec(~y))
152+
@rule sec(~x +
153+
~y) => sec(~x) * sec(~y) * csc(~x) * csc(~y) /
154+
(csc(~x) * csc(~y) - sec(~x) * sec(~y))
147155
@rule cot(~x + ~y) => (cot(~x) * cot(~y) - 1) / (cot(~x) + cot(~y))
148156
@rule sin(~x - ~y) => sin(~x) * cos(~y) - cos(~x) * sin(~y)
149157
@rule cos(~x - ~y) => cos(~x) * cos(~y) + sin(~x) * sin(~y)
150158
@rule tan(~x - ~y) => (tan(~x) - tan(~y)) / (1 + tan(~x) * tan(~y))
151-
@rule csc(~x - ~y) => sec(~x) * sec(~y) * csc(~x) * csc(~y) /
152-
(sec(~x) * csc(~y) - csc(~x) * sec(~y))
153-
@rule sec(~x - ~y) => sec(~x) * sec(~y) * csc(~x) * csc(~y) /
154-
(csc(~x) * csc(~y) + sec(~x) * sec(~y))
159+
@rule csc(~x -
160+
~y) => sec(~x) * sec(~y) * csc(~x) * csc(~y) /
161+
(sec(~x) * csc(~y) - csc(~x) * sec(~y))
162+
@rule sec(~x -
163+
~y) => sec(~x) * sec(~y) * csc(~x) * csc(~y) /
164+
(csc(~x) * csc(~y) + sec(~x) * sec(~y))
155165
@rule cot(~x - ~y) => (cot(~x) * cot(~y) + 1) / (cot(~x) - cot(~y))
156166

157167
# @rule sin(2*~x) => 2*sin(~x)*cos(~x)
@@ -239,8 +249,9 @@ rational_rules = [@rule Ω(+(~~xs)) => sum(map(Ω, ~~xs))
239249
@rule Ω(^(~x::is_poly, ~k::is_neg_int)) => expand(^(
240250
decompose_rational(~x),
241251
-~k))
242-
@rule Ω(~x / ^(~y::is_poly, ~k::is_pos_int)) => expand(~x *
243-
^(
252+
@rule Ω(~x /
253+
^(~y::is_poly, ~k::is_pos_int)) => expand(~x *
254+
^(
244255
decompose_rational(~y),
245256
~k))
246257
@rule Ω(~x / ~y::is_poly) => expand(~x * decompose_rational(~y))

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