Expression of type InSet

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 Variable
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.logic import CartExp, InSet
from proveit.numbers import Complex, Exp, Mult, Neg, e, frac, i, one, pi, sqrt, two
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
expr = InSet(ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Variable("_a", latex_format = r"{_{-}a}"))), _phase)), ket1))), CartExp(Complex, Exp(two, one)))

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^{-{_{-}a}} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right) \in \mathbb{C}^{2^{1}}

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