Expression of type Conditional ¶

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, m, rho, x
from proveit.linear_algebra import MatrixExp, MatrixMult, ScalarMult
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Exp, Mult, NaturalPos, Real, e, i, pi, two

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [rho], instance_expr = 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))), domain = Real), InSet(m, NaturalPos))

# 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\{\forall_{\rho \in \mathbb{R}}~\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)\right] \textrm{ if } m \in \mathbb{N}^+\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 11 operand: 5
2	Operation	operator: 13 operands: 4
3	ExprTuple	5
4	ExprTuple	54, 6
5	Lambda	parameter: 55 body: 8
6	Literal
7	ExprTuple	55
8	Conditional	value: 9 condition: 10
9	Operation	operator: 11 operand: 15
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15
13	Literal
14	ExprTuple	55, 16
15	Lambda	parameters: 30 body: 17
16	Literal
17	Conditional	value: 18 condition: 19
18	Operation	operator: 21 operands: 20
19	Operation	operator: 21 operands: 22
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	25, 26
23	Operation	operator: 29 operands: 27
24	Operation	operator: 31 operands: 28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 31 operands: 32
27	ExprTuple	33, 36
28	ExprTuple	34, 36
29	Literal
30	ExprTuple	42, 36
31	Literal
32	ExprTuple	35, 36
33	Operation	operator: 37 operands: 38
34	Operation	operator: 40 operands: 39
35	Operation	operator: 40 operands: 41
36	Variable
37	Literal
38	ExprTuple	42, 54
39	ExprTuple	44, 43
40	Literal
41	ExprTuple	44, 45
42	Variable
43	Operation	operator: 52 operands: 46
44	Literal
45	Operation	operator: 52 operands: 47
46	ExprTuple	49, 50, 51, 48
47	ExprTuple	49, 50, 51, 55
48	Operation	operator: 52 operands: 53
49	Literal
50	Literal
51	Literal
52	Literal
53	ExprTuple	54, 55
54	Variable
55	Variable

Expression of type Conditional¶

from the theory of proveit.linear_algebra.matrices.exponentiation¶

Expression of type Conditional ¶

from the theory of proveit.linear_algebra.matrices.exponentiation ¶