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 _ket_u, _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(), _ket_u)

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), \lvert u \rangle\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	ExprRange	lambda_map: 3 start_index: 4 end_index: 25
2	Literal
3	Lambda	parameter: 48 body: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 22 operands: 8
6	Literal
7	ExprTuple	9, 35
8	ExprTuple	10, 11
9	Operation	operator: 46 operand: 16
10	Operation	operator: 28 operands: 13
11	Operation	operator: 14 operands: 15
12	ExprTuple	16
13	ExprTuple	35, 17
14	Literal
15	ExprTuple	18, 19
16	Variable
17	Operation	operator: 42 operands: 20
18	Operation	operator: 31 operand: 25
19	Operation	operator: 22 operands: 23
20	ExprTuple	44, 24
21	ExprTuple	25
22	Literal
23	ExprTuple	26, 27
24	Operation	operator: 28 operands: 29
25	Literal
26	Operation	operator: 42 operands: 30
27	Operation	operator: 31 operand: 35
28	Literal
29	ExprTuple	35, 44
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	35
33	Literal
34	Operation	operator: 36 operands: 37
35	Literal
36	Literal
37	ExprTuple	44, 38, 39, 40, 41
38	Literal
39	Literal
40	Operation	operator: 42 operands: 43
41	Literal
42	Literal
43	ExprTuple	44, 45
44	Literal
45	Operation	operator: 46 operand: 48
46	Literal
47	ExprTuple	48
48	Variable