CAS(C)

Experimental CAS in C

Note: ill be redesigning this thing to make it easier to read ard dec period

Goal: Implement solving of equations with steps that a human can understand

Expression types:

0. variable
1. number
2. a+b
3. a-b
4. a*b
5. a/b
6. a^b
7. aroot(b)
8. log_a(b)
9. ln(a)

Simplification algorithms:

• Addition and multiplication commutativity
• subtraction->addition, division->multiplication, root->exp
• Expanding multiplication and exponentiation
• Factoring common terms for addition and multiplication

Ordering

Different types are just compared by a->type - b->type

Same types but different lengths are just compared by a->len - b->len

Numbers and variables are just compared by a - b

Else compare function recursively scans tree, using pre-order search

Parser

Uses shunting yard to parse from string to rpn

Converts rpn to syntax tree

Polynomial solver

Durand-Kerner method, find complex and repeated roots too

ToDo

• Make code neater, have more headers so less functions clumped together
• Adding more functions
• Improve shunting yard algorithm
  • Unary subtraction
  • Making code easier to change
  • Tokenizing to array
  • Use array instead of stack and queue may be better?
• Parsing log(x) instead of log_(a)(b)
• Integration(definite, indefinite, contour)
• Differential equations

Future ideas

• Integral/ODE/etc. using neural nets