Expression of type Equals

from the theory of proveit.physics.quantum.QPE

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.linear_algebra import MatrixMult, ScalarMult
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, e, i, pi, two
from proveit.physics.quantum.QPE import _U, _ket_u, _phase

# build up the expression from sub-expressions
expr = Equals(MatrixMult(_U, _ket_u), ScalarMult(Exp(e, Mult(two, pi, i, _phase)), _ket_u))

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(U \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert u \rangle\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 11
7	Literal
8	ExprTuple	10, 11
9	Literal
10	Operation	operator: 12 operands: 13
11	Literal
12	Literal
13	ExprTuple	14, 15
14	Literal
15	Operation	operator: 16 operands: 17
16	Literal
17	ExprTuple	18, 19, 20, 21
18	Literal
19	Literal
20	Literal
21	Literal