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 ExprRange, ExprTuple, Variable, t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Add, Exp, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(ExprRange(sub_expr1, ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1))), Add(Neg(t), one), zero).with_decreasing_order())

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(\left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 1} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right), \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{t - 2} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right), \ldots, \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{0} \cdot \varphi} \cdot \lvert 1 \rangle\right)\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	ExprRange	lambda_map: 2 start_index: 3 end_index: 24
2	Lambda	parameter: 47 body: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 21 operands: 7
5	Literal
6	ExprTuple	8, 34
7	ExprTuple	9, 10
8	Operation	operator: 45 operand: 15
9	Operation	operator: 27 operands: 12
10	Operation	operator: 13 operands: 14
11	ExprTuple	15
12	ExprTuple	34, 16
13	Literal
14	ExprTuple	17, 18
15	Variable
16	Operation	operator: 41 operands: 19
17	Operation	operator: 30 operand: 24
18	Operation	operator: 21 operands: 22
19	ExprTuple	43, 23
20	ExprTuple	24
21	Literal
22	ExprTuple	25, 26
23	Operation	operator: 27 operands: 28
24	Literal
25	Operation	operator: 41 operands: 29
26	Operation	operator: 30 operand: 34
27	Literal
28	ExprTuple	34, 43
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	34
32	Literal
33	Operation	operator: 35 operands: 36
34	Literal
35	Literal
36	ExprTuple	43, 37, 38, 39, 40
37	Literal
38	Literal
39	Operation	operator: 41 operands: 42
40	Literal
41	Literal
42	ExprTuple	43, 44
43	Literal
44	Operation	operator: 45 operand: 47
45	Literal
46	ExprTuple	47
47	Variable