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 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))), Neg(t), 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} \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 - 1} \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: 21
2	Lambda	parameter: 44 body: 4
3	Operation	operator: 42 operand: 7
4	Operation	operator: 18 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9
7	Variable
8	Operation	operator: 24 operands: 10
9	Operation	operator: 11 operands: 12
10	ExprTuple	31, 13
11	Literal
12	ExprTuple	14, 15
13	Operation	operator: 38 operands: 16
14	Operation	operator: 27 operand: 21
15	Operation	operator: 18 operands: 19
16	ExprTuple	40, 20
17	ExprTuple	21
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 24 operands: 25
21	Literal
22	Operation	operator: 38 operands: 26
23	Operation	operator: 27 operand: 31
24	Literal
25	ExprTuple	31, 40
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	31
29	Literal
30	Operation	operator: 32 operands: 33
31	Literal
32	Literal
33	ExprTuple	40, 34, 35, 36, 37
34	Literal
35	Literal
36	Operation	operator: 38 operands: 39
37	Literal
38	Literal
39	ExprTuple	40, 41
40	Literal
41	Operation	operator: 42 operand: 44
42	Literal
43	ExprTuple	44
44	Variable