Expression of type ExprTuple

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

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

\left(\alpha_{m ~\textup{mod}~ 2^{t}}, \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)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 31 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Operation	operator: 9 operands: 48
7	Operation	operator: 47 operands: 10
8	Operation	operator: 11 operand: 13
9	Literal
10	ExprTuple	43, 50
11	Literal
12	ExprTuple	13
13	Lambda	parameter: 22 body: 15
14	ExprTuple	22
15	Conditional	value: 16 condition: 17
16	Operation	operator: 51 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	22, 23
21	Operation	operator: 51 operands: 24
22	Variable
23	Operation	operator: 25 operands: 26
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	29, 30
27	Literal
28	Operation	operator: 31 operands: 32
29	Literal
30	Operation	operator: 38 operands: 33
31	Literal
32	ExprTuple	53, 34, 35, 36
33	ExprTuple	50, 37
34	Literal
35	Literal
36	Operation	operator: 38 operands: 39
37	Operation	operator: 44 operand: 43
38	Literal
39	ExprTuple	41, 42
40	ExprTuple	43
41	Literal
42	Operation	operator: 44 operand: 46
43	Literal
44	Literal
45	ExprTuple	46
46	Operation	operator: 47 operands: 48
47	Literal
48	ExprTuple	49, 50
49	Variable
50	Operation	operator: 51 operands: 52
51	Literal
52	ExprTuple	53, 54
53	Literal
54	Literal