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, Neg, Sum, e, frac, i, one, pi, 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 = Mult(Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t))), Exp(e, Mult(two, pi, i, _phase, 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} \left(\mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k}\right)\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: 41 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 34 operands: 4
3	Operation	operator: 5 operand: 7
4	ExprTuple	40, 39
5	Literal
6	ExprTuple	7
7	Lambda	parameter: 47 body: 9
8	ExprTuple	47
9	Conditional	value: 10 condition: 11
10	Operation	operator: 41 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	47, 17
15	Operation	operator: 43 operands: 18
16	Operation	operator: 43 operands: 19
17	Operation	operator: 20 operands: 21
18	ExprTuple	23, 22
19	ExprTuple	23, 24
20	Literal
21	ExprTuple	25, 26
22	Operation	operator: 36 operand: 31
23	Literal
24	Operation	operator: 41 operands: 28
25	Literal
26	Operation	operator: 29 operands: 30
27	ExprTuple	31
28	ExprTuple	49, 45, 46, 32, 47
29	Literal
30	ExprTuple	39, 33
31	Operation	operator: 34 operands: 35
32	Literal
33	Operation	operator: 36 operand: 40
34	Literal
35	ExprTuple	38, 39
36	Literal
37	ExprTuple	40
38	Operation	operator: 41 operands: 42
39	Operation	operator: 43 operands: 44
40	Literal
41	Literal
42	ExprTuple	49, 45, 46, 47, 48
43	Literal
44	ExprTuple	49, 50
45	Literal
46	Literal
47	Variable
48	Variable
49	Literal
50	Literal