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 import ExprRange, Variable, k, t
from proveit.core_expr_types import Len
from proveit.linear_algebra import ScalarMult
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, e, i, one, pi, two
from proveit.physics.quantum import NumKet, ket0
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [ket0, ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, t))]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, two)]))

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(\lvert 0 \rangle, \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right)| = |\left(1, \ldots, 2\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: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10
8	Operation	operator: 11 operand: 17
9	Operation	operator: 13 operands: 14
10	ExprRange	lambda_map: 15 start_index: 16 end_index: 31
11	Literal
12	ExprTuple	17
13	Literal
14	ExprTuple	18, 19
15	Lambda	parameter: 25 body: 25
16	Literal
17	Literal
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	ExprTuple	25
21	Literal
22	ExprTuple	26, 27
23	Literal
24	ExprTuple	35, 28
25	Variable
26	Literal
27	Operation	operator: 29 operands: 30
28	Variable
29	Literal
30	ExprTuple	31, 32, 33, 34, 35
31	Literal
32	Literal
33	Literal
34	Literal
35	Variable