• Differential Equations
• Term rewriting
• Computer Numbers

https://en.wikipedia.org/wiki/Computer_algebra_system

# Systems

FriCAS Axiom

https://twitter.com/jjcarett2/status/1598627244292935681?s=20&t=5JLrAKIKjXwiuDermxDT0g Schwartz-Zippel and polynomial identity testing https://arxiv.org/abs/2211.09691

# Sympy

https://news.ycombinator.com/item?id=37430759 towards a new sympy interesting. Automatic evaluation is a perf problem. Moving towards using poly algebraic structures than generic symbolic featurz

Symengine

https://www.philipzucker.com/a-smattering-of-physics-in-sympy/

sympy makes math fun agan

from sympy import *
init_printing()
t,a,d,vf,vi = symbols("t a d vf vi")
e1 = Eq(d , vi * t + 1/2 * a * t ** 2)
tsub = solve(Eq(vf , vi + a * t),t)
print(tsub) # This is assuming a is nonzero though.
expand(simplify(e1.subs(t,tsub)))


https://leanprover.github.io/theorem_proving_in_lean4/conv.html


class Proof():
def __init__(self,expr):
self.steps = []
self.ctx = []
self.expr = expr
def arg(self,n):

def cong(self): #pop up
def simp(self):
self.steps.append("simp")
self.expr = simplify(self.expr)
def expand(self):
def factor(self):
def comm(self):
def assoc(self):
def apply(self,eq):

def subst(self,e):
assert sympy.Eq(e)
self.steps.append(("rw", e))
self.expr = e
def pprint(self):
map(latex, self.steps)



# Integration

https://en.wikipedia.org/wiki/Symbolic_integration

Risch algorithm https://en.wikipedia.org/wiki/Risch_algorithm “heuristic risch”

https://docs.sympy.org/latest/modules/integrals/integrals.html Meijer G functions. Closed form for definite integrals even in compound terms They also have “hand” mode which returns steps

Schanuel Conjecture

# Maxima

echo "
print(hello);
expand ((x + y)^6);
factor (x^6 - 1);
exp(%i*%pi);
linsolve ([3*x + 4*y = 7, 2*x + a*y = 13], [x, y]);
solve (x^3 - 3*x^2 + 5*x = 15, x);
eq_2: 3*x + y = 1$#$ is silent
plot2d (sin(x)/x, [x, -20, 20])\$
?? integ
quit();
" | maxima

% is most recent calculated
Also can refer to by assigned number


# Axiom

https://github.com/daly/axiom Hmm I can’t get it too install. soorrrry axiom

# Misc

http://www.sc-square.org/schools.html