# a matrix-multiplication algorithm that is/will/would asymptotically

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#### taraa

##### Senior Member
Hi
Why is "is" used in "that is asymptotically" not "will" or "would" like another "will"s or "would" in the text?
"Professor Caesar wishes to develop a matrix-multiplication algorithm that is asymptotically faster than Strassen’s algorithm. His algorithm will use the divideand-conquer method, dividing each matrix into pieces of size n/4 * n/4, and the divide and combine steps together will take theta(n2) time. He needs to determine how many subproblems his algorithm has to create in order to beat Strassen’s algorithm. If his algorithm creates a subproblems, then the recurrence for the running time T(n) becomes T(n)= aT(n/4)+theta(n2). What is the largest integer value of a for which Professor Caesar’s algorithm would be asymptotically faster than Strassen’s algorithm?"

• #### grassy

##### Senior Member
You could use will be in the first sentence. I don't think that would change the meaning in any significant way.

#### taraa

##### Senior Member
You could use will be in the first sentence. I don't think that would change the meaning in any significant way.
Thank you very much
Can "would" too?

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#### Wandering JJ

##### Senior Member
You mean in the opening sentence. I don't think so, without changing the tense of the opening: "Professor Caesar wanted/wished to develop a matrix-multiplication algorithm that would be asymptotically faster... "

#### entangledbank

##### Senior Member
If you want a difference, you could think of the 'will' parts as steps in a process: first it does this, then it does that . . . But it hasn't been designed yet, so first it will do this, then it will do that . . . At the end of the design process, he has an algorithm that is (timelessly, Platonically) faster than Strassen's. This timeless result is stated as an objective before the steps are laid out. But really, the difference is very minor*.

* It's a minor of a matrix. (How many matrix jokes do you read here?)

#### taraa

##### Senior Member
You mean in the opening sentence. I don't think so, without changing the tense of the opening: "Professor Caesar wanted/wished to develop a matrix-multiplication algorithm that would be asymptotically faster... "
If you want a difference, you could think of the 'will' parts as steps in a process: first it does this, then it does that . . . But it hasn't been designed yet, so first it will do this, then it will do that . . . At the end of the design process, he has an algorithm that is (timelessly, Platonically) faster than Strassen's. This timeless result is stated as an objective before the steps are laid out. But really, the difference is very minor*.

* It's a minor of a matrix. (How many matrix jokes do you read here?)
Thank you both very much
If the algorithms hasn't designed yet, how they say "that is asymptotically" not "will be"?
Sorry entngledbank I can understand your meaning by "How many matrix jokes do you read here?"?

#### Edinburgher

##### Senior Member
The timelessness aspect justifies the present tense. You could ask "Does there exist {or "Is there"} an algorithm that is faster than Strassen's?", and you might answer yes, and Prof Caesar wants to develop it.
Algorithms have, in some sense, an existence that is permanent. They kind of "exist" even before they have been discovered by anyone. Prof Caesar's "development" of it is perhaps more like a discovery than a creation.

#### grassy

##### Senior Member
Prof Caesar's "development" of it is perhaps more like a discovery than a creation.
The timeless question: is mathematics discovered or invented?

#### Wandering JJ

##### Senior Member
Thank you both very much
If the algorithms hasn't designed yet, how they say "that is asymptotically" not "will be"?
It's 'is' because it is the end result. Let's keep it simple and without asymptotes!
"We will be having friends round on Saturday and I'm going to prepare a meal that is the best they have ever tasted." OK, as expressed above, you could say "will be", but what I've written is much more natural, especially when in the spoken language, you would say "... I'm going to prepare a meal that's the best they've ever tasted."

#### PaulQ

##### Senior Member
that is asymptotically faster - that [in its completed state] has a state of being asymptotically faster.

"... that is asymptotically faster" is an adjectival clause - as a consequence, its tense is not dependent on the main clause - an adjectival clause's job is to describe its noun - nothing else.

#### taraa

##### Senior Member
The timelessness aspect justifies the present tense. You could ask "Does there exist {or "Is there"} an algorithm that is faster than Strassen's?", and you might answer yes, and Prof Caesar wants to develop it.
Algorithms have, in some sense, an existence that is permanent. They kind of "exist" even before they have been discovered by anyone. Prof Caesar's "development" of it is perhaps more like a discovery than a creation.
Isn't the algorithm designed yet, right?
It's 'is' because it is the end result. Let's keep it simple and without asymptotes!
"We will be having friends round on Saturday and I'm going to prepare a meal that is the best they have ever tasted." OK, as expressed above, you could say "will be", but what I've written is much more natural, especially when in the spoken language, you would say "... I'm going to prepare a meal that's the best they've ever tasted."
that is asymptotically faster - that [in its completed state] has a state of being asymptotically faster.

"... that is asymptotically faster" is an adjectival clause - as a consequence, its tense is not dependent on the main clause - an adjectival clause's job is to describe its noun - nothing else.
Thank you both very much

#### Chasint

##### Senior Member
that is asymptotically faster - that [in its completed state] has a state of being asymptotically faster.

"... that is asymptotically faster" is an adjectival clause - as a consequence, its tense is not dependent on the main clause - an adjectival clause's job is to describe its noun - nothing else.
This seems to be the key. There are plenty of very ordinary examples that I can think of.

I intend to buy a car that is bigger than the one I have now.

I shall buy a car that runs faster than the one have now.

Mary Berry will bake you a cake that tastes delicious.

A man who is tall, dark, handsome and rich, will come into your life.

#### taraa

##### Senior Member
This seems to be the key. There are plenty of very ordinary examples that I can think of.

I intend to buy a car that is bigger than the one I have now.

I shall buy a car that runs faster than the one have now.

Mary Berry will bake you a cake that tastes delicious.

A man who is tall, dark, handsome and rich, will come into your life.
Thank you very much

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