math-help

Name: math-help
Author: parcadei

3.9kstars297forks

How to install math-help?

parcadei/continuous-claude-v3/math-help

$npx -y skills add parcadei/Continuous-Claude-v3 --skill math-help

Installs into the current project.

Summary

Guide to the math cognitive stack - what tools exist and when to use each

Files · 1

View on GitHub

SKILL.md

1	# Math Cognitive Stack Guide
2
3	Cognitive prosthetics for exact mathematical computation. This guide helps you choose the right tool for your math task.
4
5	## Quick Reference
6
7	\| I want to... \| Use this \| Example \|
8	\|--------------\|----------\|---------\|
9	\| Solve equations \| sympy_compute.py solve \| `solve "x**2 - 4 = 0" --var x` \|
10	\| Integrate/differentiate \| sympy_compute.py \| `integrate "sin(x)" --var x` \|
11	\| Compute limits \| sympy_compute.py limit \| `limit "sin(x)/x" --var x --to 0` \|
12	\| Matrix operations \| sympy_compute.py / numpy_compute.py \| `det "[[1,2],[3,4]]"` \|
13	\| Verify a reasoning step \| math_scratchpad.py verify \| `verify "x = 2 implies x^2 = 4"` \|
14	\| Check a proof chain \| math_scratchpad.py chain \| `chain --steps '[...]'` \|
15	\| Get progressive hints \| math_tutor.py hint \| `hint "Solve x^2 - 4 = 0" --level 2` \|
16	\| Generate practice problems \| math_tutor.py generate \| `generate --topic algebra --difficulty 2` \|
17	\| Prove a theorem (constraints) \| z3_solve.py prove \| `prove "x + y == y + x" --vars x y` \|
18	\| Check satisfiability \| z3_solve.py sat \| `sat "x > 0, x < 10, x*x == 49"` \|
19	\| Optimize with constraints \| z3_solve.py optimize \| `optimize "x + y" --constraints "..."` \|
20	\| Plot 2D/3D functions \| math_plot.py \| `plot2d "sin(x)" --range -10 10` \|
21	\| Arbitrary precision \| mpmath_compute.py \| `pi --dps 100` \|
22	\| Numerical optimization \| scipy_compute.py \| `minimize "x*2 + 2x" "5"` \|
23	\| Formal machine proof \| Lean 4 (lean4 skill) \| `/lean4` \|
24
25	## The Five Layers
26
27	### Layer 1: SymPy (Symbolic Algebra)
28
29	When: Exact algebraic computation - solving, calculus, simplification, matrix algebra.
30
31	Key Commands:
32	```bash
33	# Solve equation
34	uv run python -m runtime.harness scripts/sympy_compute.py \
35	solve "x*2 - 5x + 6 = 0" --var x --domain real
36
37	# Integrate
38	uv run python -m runtime.harness scripts/sympy_compute.py \
39	integrate "sin(x)" --var x
40
41	# Definite integral
42	uv run python -m runtime.harness scripts/sympy_compute.py \
43	integrate "x**2" --var x --bounds 0 1
44
45	# Differentiate (2nd order)
46	uv run python -m runtime.harness scripts/sympy_compute.py \
47	diff "x**3" --var x --order 2
48
49	# Simplify (trig strategy)
50	uv run python -m runtime.harness scripts/sympy_compute.py \
51	simplify "sin(x)2 + cos(x)2" --strategy trig
52
53	# Limit
54	uv run python -m runtime.harness scripts/sympy_compute.py \
55	limit "sin(x)/x" --var x --to 0
56
57	# Matrix eigenvalues
58	uv run python -m runtime.harness scripts/sympy_compute.py \
59	eigenvalues "[[1,2],[3,4]]"
60	```
61
62	Best For: Closed-form solutions, calculus, exact algebra.
63
64	### Layer 2: Z3 (Constraint Solving & Theorem Proving)
65
66	When: Proving theorems, checking satisfiability, constraint optimization.
67
68	Key Commands:
69	```bash
70	# Prove commutativity
71	uv run python -m runtime.harness scripts/cc_math/z3_solve.py \
72	prove "x + y == y + x" --vars x y --type int
73
74	# Check satisfiability
75	uv run python -m runtime.harness scripts/cc_math/z3_solve.py \
76	sat "x > 0, x < 10, x*x == 49" --type int
77
78	# Optimize
79	uv run python -m runtime.harness scripts/cc_math/z3_solve.py \
80	optimize "x + y" --constraints "x >= 0, y >= 0, x + y <= 100" \
81	--direction maximize --type real
82	```
83
84	Best For: Logical proofs, constraint satisfaction, optimization with constraints.
85
86	### Layer 3: Math Scratchpad (Reasoning Verification)
87
88	When: Verifying step-by-step reasoning, checking derivation chains.
89
90	Key Commands:
91	```bash
92	# Verify single step
93	uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py \
94	verify "x = 2 implies x^2 = 4"
95
96	# Verify with context
97	uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py \
98	verify "x^2 = 4" --context '{"x": 2}'
99
100	# Verify chain of reasoning
101	uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py \
102	chain --steps '["x^2 - 4 = 0", "(x-2)(x+2) = 0", "x = 2 or x = -2"]'
103
104	# Explain a step
105	uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py \
106	explain "d/dx(x^3) = 3*x^2"
107	```
108
109	Best For: Checking your work, validating derivations, step-by-step verification.
110
111	### Layer 4: Math Tutor (Educational)
112
113	When: Learning, getting hints, generating practice problems.
114
115	Key Commands:
116	```bash
117	# Step-by-step solution
118	uv run python scripts/cc_math/math_tutor.py steps "x*2 - 5x + 6 = 0" --operation solve
119
120	# Progressive hint (level 1-5)
121	uv run python scripts/cc_math/math_tutor.py hint "Solve x**2 - 4 = 0" --level 2
122
123	# Generate practice problem
124	uv run python scripts/cc_math/math_tutor.py generate --topic algebra --difficulty 2
125	```
126
127	Best For: Learning, tutoring, practice.
128
129	### Layer 5: Lean 4 (Formal Proofs)
130
131	When: Rigorous machine-verified mathematical proofs, category theory, type theory.
132
133	Access: Use `/lean4` skill for full documentation.
134
135	Best For:

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math-help

3.9kstars297forks

View on GitHub

How to install math-help?

parcadei/continuous-claude-v3/math-help

$npx -y skills add parcadei/Continuous-Claude-v3 --skill math-help

Installs into the current project.

Summary

Guide to the math cognitive stack - what tools exist and when to use each

Files · 1

View on GitHub

SKILL.md

1	# Math Cognitive Stack Guide
2
3	Cognitive prosthetics for exact mathematical computation. This guide helps you choose the right tool for your math task.
4
5	## Quick Reference
6
7	\| I want to... \| Use this \| Example \|
8	\|--------------\|----------\|---------\|
9	\| Solve equations \| sympy_compute.py solve \| `solve "x**2 - 4 = 0" --var x` \|
10	\| Integrate/differentiate \| sympy_compute.py \| `integrate "sin(x)" --var x` \|
11	\| Compute limits \| sympy_compute.py limit \| `limit "sin(x)/x" --var x --to 0` \|
12	\| Matrix operations \| sympy_compute.py / numpy_compute.py \| `det "[[1,2],[3,4]]"` \|
13	\| Verify a reasoning step \| math_scratchpad.py verify \| `verify "x = 2 implies x^2 = 4"` \|
14	\| Check a proof chain \| math_scratchpad.py chain \| `chain --steps '[...]'` \|
15	\| Get progressive hints \| math_tutor.py hint \| `hint "Solve x^2 - 4 = 0" --level 2` \|
16	\| Generate practice problems \| math_tutor.py generate \| `generate --topic algebra --difficulty 2` \|
17	\| Prove a theorem (constraints) \| z3_solve.py prove \| `prove "x + y == y + x" --vars x y` \|
18	\| Check satisfiability \| z3_solve.py sat \| `sat "x > 0, x < 10, x*x == 49"` \|
19	\| Optimize with constraints \| z3_solve.py optimize \| `optimize "x + y" --constraints "..."` \|
20	\| Plot 2D/3D functions \| math_plot.py \| `plot2d "sin(x)" --range -10 10` \|
21	\| Arbitrary precision \| mpmath_compute.py \| `pi --dps 100` \|
22	\| Numerical optimization \| scipy_compute.py \| `minimize "x*2 + 2x" "5"` \|
23	\| Formal machine proof \| Lean 4 (lean4 skill) \| `/lean4` \|
24
25	## The Five Layers
26
27	### Layer 1: SymPy (Symbolic Algebra)
28
29	When: Exact algebraic computation - solving, calculus, simplification, matrix algebra.
30
31	Key Commands:
32	```bash
33	# Solve equation
34	uv run python -m runtime.harness scripts/sympy_compute.py \
35	solve "x*2 - 5x + 6 = 0" --var x --domain real
36
37	# Integrate
38	uv run python -m runtime.harness scripts/sympy_compute.py \
39	integrate "sin(x)" --var x
40
41	# Definite integral
42	uv run python -m runtime.harness scripts/sympy_compute.py \
43	integrate "x**2" --var x --bounds 0 1
44
45	# Differentiate (2nd order)
46	uv run python -m runtime.harness scripts/sympy_compute.py \
47	diff "x**3" --var x --order 2
48
49	# Simplify (trig strategy)
50	uv run python -m runtime.harness scripts/sympy_compute.py \
51	simplify "sin(x)2 + cos(x)2" --strategy trig
52
53	# Limit
54	uv run python -m runtime.harness scripts/sympy_compute.py \
55	limit "sin(x)/x" --var x --to 0
56
57	# Matrix eigenvalues
58	uv run python -m runtime.harness scripts/sympy_compute.py \
59	eigenvalues "[[1,2],[3,4]]"
60	```
61
62	Best For: Closed-form solutions, calculus, exact algebra.
63
64	### Layer 2: Z3 (Constraint Solving & Theorem Proving)
65
66	When: Proving theorems, checking satisfiability, constraint optimization.
67
68	Key Commands:
69	```bash
70	# Prove commutativity
71	uv run python -m runtime.harness scripts/cc_math/z3_solve.py \
72	prove "x + y == y + x" --vars x y --type int
73
74	# Check satisfiability
75	uv run python -m runtime.harness scripts/cc_math/z3_solve.py \
76	sat "x > 0, x < 10, x*x == 49" --type int
77
78	# Optimize
79	uv run python -m runtime.harness scripts/cc_math/z3_solve.py \
80	optimize "x + y" --constraints "x >= 0, y >= 0, x + y <= 100" \
81	--direction maximize --type real
82	```
83
84	Best For: Logical proofs, constraint satisfaction, optimization with constraints.
85
86	### Layer 3: Math Scratchpad (Reasoning Verification)
87
88	When: Verifying step-by-step reasoning, checking derivation chains.
89
90	Key Commands:
91	```bash
92	# Verify single step
93	uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py \
94	verify "x = 2 implies x^2 = 4"
95
96	# Verify with context
97	uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py \
98	verify "x^2 = 4" --context '{"x": 2}'
99
100	# Verify chain of reasoning
101	uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py \
102	chain --steps '["x^2 - 4 = 0", "(x-2)(x+2) = 0", "x = 2 or x = -2"]'
103
104	# Explain a step
105	uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py \
106	explain "d/dx(x^3) = 3*x^2"
107	```
108
109	Best For: Checking your work, validating derivations, step-by-step verification.
110
111	### Layer 4: Math Tutor (Educational)
112
113	When: Learning, getting hints, generating practice problems.
114
115	Key Commands:
116	```bash
117	# Step-by-step solution
118	uv run python scripts/cc_math/math_tutor.py steps "x*2 - 5x + 6 = 0" --operation solve
119
120	# Progressive hint (level 1-5)
121	uv run python scripts/cc_math/math_tutor.py hint "Solve x**2 - 4 = 0" --level 2
122
123	# Generate practice problem
124	uv run python scripts/cc_math/math_tutor.py generate --topic algebra --difficulty 2
125	```
126
127	Best For: Learning, tutoring, practice.
128
129	### Layer 5: Lean 4 (Formal Proofs)
130
131	When: Rigorous machine-verified mathematical proofs, category theory, type theory.
132
133	Access: Use `/lean4` skill for full documentation.
134
135	Best For:

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