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 k, t
from proveit.linear_algebra import ScalarMult, TensorProd, VecSum
from proveit.logic import CartExp, InSet
from proveit.numbers import Complex, Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet, QubitSpace, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = InSet(VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), TensorProd(ket1, NumKet(k, t))), domain = Interval(zero, subtract(two_pow_t, one))), TensorProd(QubitSpace, CartExp(Complex, two_pow_t)))

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(\sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \left(\lvert 1 \rangle {\otimes} \lvert k \rangle_{t}\right)\right)\right) \in \left(\mathbb{C}^{2} {\otimes} \mathbb{C}^{2^{t}}\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: 20 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 4 operand: 7
3	Operation	operator: 26 operands: 6
4	Literal
5	ExprTuple	7
6	ExprTuple	8, 9
7	Lambda	parameter: 46 body: 11
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	ExprTuple	46
11	Conditional	value: 15 condition: 16
12	ExprTuple	17, 53
13	Literal
14	ExprTuple	17, 47
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	46, 24
22	Operation	operator: 49 operands: 25
23	Operation	operator: 26 operands: 27
24	Operation	operator: 28 operands: 29
25	ExprTuple	30, 31
26	Literal
27	ExprTuple	32, 33
28	Literal
29	ExprTuple	34, 35
30	Literal
31	Operation	operator: 36 operands: 37
32	Operation	operator: 38 operand: 55
33	Operation	operator: 39 operands: 40
34	Literal
35	Operation	operator: 41 operands: 42
36	Literal
37	ExprTuple	53, 43, 44, 45, 46
38	Literal
39	Literal
40	ExprTuple	46, 54
41	Literal
42	ExprTuple	47, 48
43	Literal
44	Literal
45	Literal
46	Variable
47	Operation	operator: 49 operands: 50
48	Operation	operator: 51 operand: 55
49	Literal
50	ExprTuple	53, 54
51	Literal
52	ExprTuple	55
53	Literal
54	Variable
55	Literal