Expression of type Sum

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, pi, subtract, two
from proveit.physics.quantum.QPE import _m_domain, _phase, _two_pow_t

# build up the expression from sub-expressions
expr = 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())

\sum_{k = 0}^{2^{t} - 1} (\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\varphi - \frac{m}{2^{t}}\right)})^{k}

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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