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 Add, Exp, Mult, e, frac, i, one, pi, subtract, two
from proveit.physics.quantum import QubitSpace, ket0, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = InSet(ScalarMult(frac(one, Exp(two, subtract(frac(Add(t, one), two), frac(t, two)))), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), 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(\frac{1}{2^{\frac{t + 1}{2} - \frac{t}{2}}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \cdot \lvert 1 \rangle\right)\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: 19 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 51
8	Operation	operator: 46 operands: 11
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	50, 14
12	Literal
13	ExprTuple	15, 16
14	Operation	operator: 48 operands: 17
15	Operation	operator: 27 operand: 22
16	Operation	operator: 19 operands: 20
17	ExprTuple	51, 21
18	ExprTuple	22
19	Literal
20	ExprTuple	23, 24
21	Operation	operator: 44 operands: 25
22	Literal
23	Operation	operator: 48 operands: 26
24	Operation	operator: 27 operand: 50
25	ExprTuple	29, 30
26	ExprTuple	31, 32
27	Literal
28	ExprTuple	50
29	Operation	operator: 46 operands: 33
30	Operation	operator: 34 operand: 39
31	Literal
32	Operation	operator: 36 operands: 37
33	ExprTuple	38, 51
34	Literal
35	ExprTuple	39
36	Literal
37	ExprTuple	51, 40, 41, 42, 43
38	Operation	operator: 44 operands: 45
39	Operation	operator: 46 operands: 47
40	Literal
41	Literal
42	Literal
43	Operation	operator: 48 operands: 49
44	Literal
45	ExprTuple	52, 50
46	Literal
47	ExprTuple	52, 51
48	Literal
49	ExprTuple	51, 52
50	Literal
51	Literal
52	Variable