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, t
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.numbers import Exp, Interval, Mult, e, frac, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(ScalarMult(frac(one, Exp(two, frac(t, two))), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, t)), domain = Interval(zero, subtract(two_pow_t, one)))))

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

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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