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, 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(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(\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)

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