Expression of type ExprTuple

from the theory of proveit.linear_algebra.matrices.exponentiation

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import A, Conditional, ExprTuple, Lambda, m, rho, x
from proveit.linear_algebra import MatrixExp, MatrixMult, ScalarMult
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Exp, Mult, Real, e, i, pi, two

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(rho, Conditional(Forall(instance_param_or_params = [A, x], instance_expr = Equals(MatrixMult(MatrixExp(A, m), x), ScalarMult(Exp(e, Mult(two, pi, i, Mult(m, rho))), x)), condition = Equals(MatrixMult(A, x), ScalarMult(Exp(e, Mult(two, pi, i, rho)), x))), InSet(rho, Real))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\rho \mapsto \left\{\forall_{A, x~|~\left(A \thinspace x\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \rho} \cdot x\right)}~\left(\left(A^{m} \thinspace x\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(m \cdot \rho\right)} \cdot x\right)\right) \textrm{ if } \rho \in \mathbb{R}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameter: 50 body: 3
2	ExprTuple	50
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	50, 11
10	Lambda	parameters: 25 body: 12
11	Literal
12	Conditional	value: 13 condition: 14
13	Operation	operator: 16 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20, 21
18	Operation	operator: 24 operands: 22
19	Operation	operator: 26 operands: 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operands: 27
22	ExprTuple	28, 31
23	ExprTuple	29, 31
24	Literal
25	ExprTuple	37, 31
26	Literal
27	ExprTuple	30, 31
28	Operation	operator: 32 operands: 33
29	Operation	operator: 35 operands: 34
30	Operation	operator: 35 operands: 36
31	Variable
32	Literal
33	ExprTuple	37, 49
34	ExprTuple	39, 38
35	Literal
36	ExprTuple	39, 40
37	Variable
38	Operation	operator: 47 operands: 41
39	Literal
40	Operation	operator: 47 operands: 42
41	ExprTuple	44, 45, 46, 43
42	ExprTuple	44, 45, 46, 50
43	Operation	operator: 47 operands: 48
44	Literal
45	Literal
46	Literal
47	Literal
48	ExprTuple	49, 50
49	Variable
50	Variable