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, Real, e, i, pi, two

# build up the expression from sub-expressions
expr = 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))

# 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_{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..

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