# from the theory of proveit.physics.quantum.QPE¶

In [1]:
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.
# import Expression classes needed to build the expression
from proveit import ExprRange, ExprTuple, Variable, e
from proveit.core_expr_types import Len
from proveit.numbers import Exp, Mult, Neg, frac, one, three, two
from proveit.physics.quantum.QPE import _two_pow_t

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Len(operands = [Neg(Mult(frac(one, Exp(two, one)), _two_pow_t)), one, Neg(e)]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, three)]))

expr:
In [3]:
# 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

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(|\left(-\left(\frac{1}{2^{1}} \cdot 2^{t}\right), 1, -e\right)|, |\left(1, 2, \ldots, 3\right)|\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1, 2
1Operationoperator: 4
operands: 3
2Operationoperator: 4
operands: 5
3ExprTuple6, 30, 7
4Literal
5ExprTuple8
6Operationoperator: 10
operand: 14
7Operationoperator: 10
operand: 15
8ExprRangelambda_map: 12
start_index: 30
end_index: 13
9ExprTuple14
10Literal
11ExprTuple15
12Lambdaparameter: 19
body: 19
13Literal
14Operationoperator: 17
operands: 18
15Variable
16ExprTuple19
17Literal
18ExprTuple20, 21
19Variable
20Operationoperator: 22
operands: 23
21Operationoperator: 27
operands: 24
22Literal
23ExprTuple30, 25
24ExprTuple29, 26
25Operationoperator: 27
operands: 28
26Literal
27Literal
28ExprTuple29, 30
29Literal
30Literal