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, m
from proveit.logic import InSet
from proveit.numbers import Complex, Exp, Mult, Neg, Sum, e, frac, i, pi, two
from proveit.physics.quantum.QPE import _m_domain, _phase, _two_pow_t

# build up the expression from sub-expressions
expr = InSet(Sum(index_or_indices = [k], summand = Mult(Exp(e, Mult(two, pi, i, _phase, k)), Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t)))), domain = _m_domain), Complex)

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 \mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}}\right)\right) \in \mathbb{C}

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: 12 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 4 operand: 6
3	Literal
4	Literal
5	ExprTuple	6
6	Lambda	parameter: 46 body: 8
7	ExprTuple	46
8	Conditional	value: 9 condition: 10
9	Operation	operator: 40 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	46, 16
14	Operation	operator: 42 operands: 17
15	Operation	operator: 42 operands: 18
16	Operation	operator: 19 operands: 20
17	ExprTuple	22, 21
18	ExprTuple	22, 23
19	Literal
20	ExprTuple	24, 25
21	Operation	operator: 40 operands: 26
22	Literal
23	Operation	operator: 35 operand: 31
24	Literal
25	Operation	operator: 28 operands: 29
26	ExprTuple	48, 44, 45, 30, 46
27	ExprTuple	31
28	Literal
29	ExprTuple	38, 32
30	Literal
31	Operation	operator: 33 operands: 34
32	Operation	operator: 35 operand: 39
33	Literal
34	ExprTuple	37, 38
35	Literal
36	ExprTuple	39
37	Operation	operator: 40 operands: 41
38	Operation	operator: 42 operands: 43
39	Literal
40	Literal
41	ExprTuple	48, 44, 45, 46, 47
42	Literal
43	ExprTuple	48, 49
44	Literal
45	Literal
46	Variable
47	Variable
48	Literal
49	Literal