Expression of type Mult

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.numbers import Exp, Mult, Sum, e, frac, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import _m_domain, _phase, _two_pow_t

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

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())

\frac{1}{2^{t}} \cdot \left(\sum_{k = 0}^{2^{t} - 1} (\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\varphi - \frac{m}{2^{t}}\right)})^{k}\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',)

# display the expression information
stored_expr.expr_info()

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