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 t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.logic import InSet
from proveit.numbers import Exp, Mult, e, i, one, pi, subtract, two
from proveit.physics.quantum import QubitSpace, ket0, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
expr = InSet(VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, subtract(t, one)), _phase)), ket1)), QubitSpace)

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 + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 1} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right) \in \mathbb{C}^{2}

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, 10
7	Literal
8	ExprTuple	11, 30
9	Operation	operator: 19 operand: 15
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15
13	Literal
14	ExprTuple	16, 17
15	Literal
16	Operation	operator: 28 operands: 18
17	Operation	operator: 19 operand: 38
18	ExprTuple	20, 21
19	Literal
20	Literal
21	Operation	operator: 22 operands: 23
22	Literal
23	ExprTuple	30, 24, 25, 26, 27
24	Literal
25	Literal
26	Operation	operator: 28 operands: 29
27	Literal
28	Literal
29	ExprTuple	30, 31
30	Literal
31	Operation	operator: 32 operands: 33
32	Literal
33	ExprTuple	34, 35
34	Variable
35	Operation	operator: 36 operand: 38
36	Literal
37	ExprTuple	38
38	Literal