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 ScalarMult, VecAdd
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
sub_expr1 = frac(one, sqrt(two))
expr = Equals(ScalarMult(sub_expr1, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(zero)), _phase)), ket1))), ScalarMult(sub_expr1, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, _phase)), ket1))))

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(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-0} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right) = \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\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: 20 operands: 5
4	Operation	operator: 20 operands: 6
5	ExprTuple	8, 7
6	ExprTuple	8, 9
7	Operation	operator: 12 operands: 10
8	Operation	operator: 27 operands: 11
9	Operation	operator: 12 operands: 13
10	ExprTuple	16, 14
11	ExprTuple	35, 15
12	Literal
13	ExprTuple	16, 17
14	Operation	operator: 20 operands: 18
15	Operation	operator: 43 operands: 19
16	Operation	operator: 30 operand: 49
17	Operation	operator: 20 operands: 21
18	ExprTuple	22, 25
19	ExprTuple	45, 23
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 43 operands: 26
23	Operation	operator: 27 operands: 28
24	Operation	operator: 43 operands: 29
25	Operation	operator: 30 operand: 35
26	ExprTuple	33, 32
27	Literal
28	ExprTuple	35, 45
29	ExprTuple	33, 34
30	Literal
31	ExprTuple	35
32	Operation	operator: 37 operands: 36
33	Literal
34	Operation	operator: 37 operands: 38
35	Literal
36	ExprTuple	45, 40, 41, 39, 42
37	Literal
38	ExprTuple	45, 40, 41, 42
39	Operation	operator: 43 operands: 44
40	Literal
41	Literal
42	Literal
43	Literal
44	ExprTuple	45, 46
45	Literal
46	Operation	operator: 47 operand: 49
47	Literal
48	ExprTuple	49
49	Literal